{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## The four postulates of Quantum Mechanics\n", "\n", "In this course, our aim is to study computing devices which operate according to the laws of quantum mechanics. Developed during the early 20th century by physicists Max Planck, Albert Einstein, Erwin Schrödinger and many others, quantum mechanics is a set of mathematical laws which describe the behaviour of subatomic particles such as protons, electrons, and photons. Although the theory has proven remarkably successful since its inception, it is nevertheless notoriously counterintuitive, an aspect which we shall explore in this lecture. Quantum mechanics is based on four postulates, which describe the following four intuitive ideas: How to describe a single quantum system, how to perform quantum operations on a quantum system, how to describe multiple quantum systems, and how to measure or extract classical information from a quantum system.\n", "\n", "### Postulate 1: Individual Quantum systems\n", "\n", "Recall that in the classical world, a bit $x$ can take on one of two values: 0 or 1. In the quantum world, we immediately see a radical departure from this statement, a quantum bit, or qubit, can take on not just 0 or 1, but rather both values 0 and 1 simultaneously. This is a very deep and counterintuitive statement, so it worth reflecting on: it is like saying you can be both asleep and awake at the same time, or here on Earth and simultaneously on Mars at the same time. Indeed, relative to life as we know it, _it makes no sense!_\n", "\n", "Let us formalize this phenomenon. We begin by encoding bits 0 and 1 via the standard basis vectors $\\left|0\\right\\rangle, \\left|1\\right\\rangle \\in \\mathbb C^2$ . Then, to denote that a qubit is in states $\\left|0\\right\\rangle$ and $\\left|1\\right\\rangle$ simultaneously, we write\n", "\n", "$$\n", "\\left|0\\right\\rangle+\\left|1\\right\\rangle.\n", "$$\n", "\n", "This is called a _superposition_. More generally, we can change the “extent” to which the qubit\n", "is in state $\\left|0\\right\\rangle$ versus $\\left|0\\right\\rangle$ via _amplitudes_ $\\alpha,\\beta \\in \\mathbb C$ , i.e.\n", "\n", "$$\n", "\\left|\\psi\\right\\rangle = \\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle\n", "$$\n", "\n", "The only restriction is that $\\left|\\psi\\right\\rangle$ must be a unit vector, i.e. that $\\left|\\alpha\\right|^2+ \\left|\\beta\\right|^2 = 1$. To summarize, any unit vector in $\\mathbb C^2$ describes the state of a single qubit.\n", "\n", "Qubit is a 2-dimensional (which describes a two state system). There is no physical limitation to use qubits: One can use d-state systems, resulting in d-dimensional states (called a qudit). Qudit is described by a unit vector $\\left|\\psi\\right\\rangle \\in \\mathbb C^d$ , which can be described as\n", "\n", "$$\n", "\\left|\\psi\\right\\rangle = \\alpha_0 \\left|0\\right\\rangle + \\alpha_1 \\left|1\\right\\rangle + \\cdots + \\alpha_{d-1} \\left|d-1\\right\\rangle =\\sum_{i=0}^{d-1}\\alpha_i\\left|i\\right\\rangle\n", "$$\n", "\n", "where $\\left|i\\right\\rangle\\in \\mathbb C ^d$ denotes the _i_th computational basis vector and $\\alpha_i \\in \\mathbb C$. Since $\\left|\\psi\\right\\rangle$ is a unit vector, we have $\\sum_{i=0}^{d-1}\\left|\\alpha_i\\right|^2=1$\n", "### Postulate 2: Quantum operations\n", "\n", "We next ask: What types of operations or maps can we perform on a qubit? Since a qubit is a vector, the natural choice is a linear map, i.e. multiplication by a matrix. However, not all matrices are fair game — it turns out that nature only allows a special class of matrices known as _unitary_ matrices. A unitary matrix $U \\in \\mathcal L( \\mathbb C^ d )$ is one which satisfies $UU^\\dagger = U^\\dagger U = I$. In other words, the inverse of $U$ is simple to calculate — just take the dagger of $U$ . This immediately yields a key insight — all quantum gates (qubit operations) are _reversible_. Among the most common single qubit gates are the following, known as the _Pauli_ gates, after Austrian-Swiss physicist Wolfgang Pauli:\n", "\n", "$$\n", "X=\n", "\\begin{pmatrix}\n", "0 & 1 \\\\\n", "1 & 0\n", "\\end{pmatrix} \\qquad\n", "Y=\n", "\\begin{pmatrix}\n", "0 & -i \\\\\n", "i & 0\n", "\\end{pmatrix} \\qquad\n", "Z=\n", "\\begin{pmatrix}\n", "1 & 0 \\\\\n", "0 & -1\n", "\\end{pmatrix} \\qquad\n", "$$\n", "\n", "#### $X$ Gate\n", "\n", "The $X$ gate acts as a “quantum” NOT gate, as we see below:\n", "\n", "$$\n", "X\\left|0\\right\\rangle=\\begin{pmatrix}0 & 1 \\\\1 & 0\\end{pmatrix}\\begin{pmatrix}1 \\\\ 0 \\end{pmatrix} =\\begin{pmatrix}0 \\\\ 1 \\end{pmatrix}=\\left|1\\right\\rangle \\qquad X\\left|1\\right\\rangle=\\begin{pmatrix}0 & 1 \\\\1 & 0\\end{pmatrix}\\begin{pmatrix}0 \\\\ 1 \\end{pmatrix} =\\begin{pmatrix}1 \\\\ 0 \\end{pmatrix}=\\left|0\\right\\rangle\n", "$$\n", "\n", "$\\left|+\\right\\rangle$ and $\\left|-\\right\\rangle$ are eigenvectors of $X$ i.e. $X\\left|+\\right\\rangle=\\left|+\\right\\rangle$ and $X\\left|-\\right\\rangle=-\\left|-\\right\\rangle$. The spectral decomposition of $X$ is hence\n", "\n", "$$\n", "X=\\left|+\\right\\rangle\\left\\langle+\\right|-\\left|-\\right\\rangle\\left\\langle-\\right|\n", "$$\n", "\n", "\n", "#### $Z$ Gate\n", "\n", "The $Z$ gate, on the other hand, has no classical analogue. It acts as\n", "\n", "$$\n", "Z\\left|0\\right\\rangle=\\begin{pmatrix}1 & 0 \\\\0 & -1\\end{pmatrix}\\begin{pmatrix}1 \\\\ 0 \\end{pmatrix} =\\begin{pmatrix}1 \\\\ 0 \\end{pmatrix}=\\left|0\\right\\rangle \\qquad Z\\left|1\\right\\rangle=\\begin{pmatrix}1 & 0 \\\\0 & -1\\end{pmatrix}\\begin{pmatrix}0 \\\\ 1 \\end{pmatrix} =-\\begin{pmatrix}0 \\\\ 1 \\end{pmatrix}=-\\left|1\\right\\rangle\n", "$$\n", "\n", "In other words, Z leaves $\\left|0\\right\\rangle$ invariant, but injects a “phase” of −1 in front of $\\left|1\\right\\rangle$. This also immediately shows that $\\left|0\\right\\rangle$ and $\\left|1\\right\\rangle$ are eigenvectors of Z with eigenvalues 1 and −1, respectively.\n", "\n", "The Z gate is special in that it allows us to inject a relative phase into a quantum state. For example,\n", "\n", "$$\n", "Z\\left|+\\right\\rangle=Z\\left(\\frac{1}{\\sqrt 2} \\left|0\\right\\rangle+\\frac{1}{\\sqrt 2}\\left|1\\right\\rangle\\right)=\\frac{1}{\\sqrt 2} Z \\left|0\\right\\rangle+\\frac{1}{\\sqrt 2} Z \\left|1\\right\\rangle=\\frac{1}{\\sqrt 2} \\left|0\\right\\rangle-\\frac{1}{\\sqrt 2}\\left|1\\right\\rangle=\\left|-\\right\\rangle\n", "$$\n", "\n", "By relative phase, we mean that only the amplitude on $\\left|1\\right\\rangle$ had its sign changed (or more generally, was multiplied by a phase $e^{i\\pi} = −1$). If _all_ the amplitudes in the state were instead multiplied by $e^{i\\pi}$ , then we could simply factor out the eiπ from the entire state — in this case,we would call $e^{i\\pi}$ a global phase. It turns out that a global phase is insignificant in that it cannot be experimentally detected. A relative phase may seemingly also look unimportant - yet, as we shall see in this course, it is one of the features of quantum mechanics which allows quantum computers to outperform classical ones!\n", "\n", "#### Hadamard Gate\n", "\n", "Finally, we come to a fourth important unitary gate, the Hadamard gate:\n", "\n", "$$\n", "H=\n", "\\begin{pmatrix}\n", "1 & 1 \\\\\n", "1 & -1\n", "\\end{pmatrix}\n", "$$\n", "\n", "The Hadamard gate is special in that it creates superpositions for us. Namely, we have $H\\left|0\\right\\rangle =\\left|+\\right\\rangle$ and $H\\left|1\\right\\rangle =\\left|-\\right\\rangle$. It can also “erase” superpositions, i.e. $H\\left|+\\right\\rangle =\\left|0\\right\\rangle$ and $H\\left|-\\right\\rangle =\\left|1\\right\\rangle$ . In other words, $H$ is self-inverse — we have that $H^2 = I$ for $I$ the identity matrix. In fact, the Pauli matrices are also self-inverse.\n", "\n", "#### Quantum Circuits\n", "\n", "A _quantum circuit_ is a graphical model for depicting quantum computation. The quantum computation is represented by a sequence of quantum gates, measurements, initializations of qubits to known values, and etc. For example, here are three circuits:\n", "\n", "![Three circuit examples](images/Lecture3-fig1-lr.png)\n", "\n", "They correspond to evolutions $X\\left|\\psi\\right\\rangle $, $H\\left|\\psi\\right\\rangle$, and $HX\\left|\\psi\\right\\rangle $, respectively. Each wire in such a diagram denotes a quantum system, and a box labelled by gate $U$ depicts the action of unitary $U$ . We think of time going from left to right; for the last circuit above, note that the $X$ appears on the “left” in the circuit diagram but on the “right” in the expression $HX\\left|\\psi\\right\\rangle $; this is because $X$ should be applied first to $\\left|\\psi\\right\\rangle $, then $H$.\n", "\n", "### Postulate 3: Composite Quantum Systems\n", "\n", "Thus far, we have considered only single quantum systems, i.e. states $\\left|\\psi\\right\\rangle\\in \\mathbb{C}^d$ for $d\\geq 2$. We need multiple qubits interacting simultaneously for quantum computation. How can we mathematically describe, for example, the joint state of two qubits? The correct Linear Algebraic tool for this task is the tensor product, denoted $\\otimes$. The tensor product allows us to “stitch together” two vectors. For example when two states $\\left|\\psi\\right\\rangle,\\left|\\phi\\right\\rangle\\in \\mathbb{C}^2$ interact, it results in a larger 4-dimensional vector given by $\\left|\\psi\\right\\rangle\\otimes\\left|\\phi\\right\\rangle\\in \\mathbb{C}^4$ . Formally, we have $\\mathbb{C}^2\\otimes\\mathbb{C}^2=\\mathbb{C}^{2\\times2}$ . In other words, the entries of a vector $\\left|\\psi\\right\\rangle\\otimes\\left|\\phi\\right\\rangle\\in \\mathbb{C}^2\\otimes\\mathbb{C}^2$ can be referenced via a pair of indices $(i, j)$ for $i, j \\in {0, 1}$, and the specific rule for doing so is\n", "\n", "$$\n", "\\left(\\left|\\psi\\right\\rangle\\otimes\\left|\\phi\\right\\rangle\\right)(i,j):=\\psi_i\\phi_j\n", "$$\n", "\n", "where recall $\\psi_i$ and $\\phi_j$ are the entries of $\\left|\\psi\\right\\rangle$ and $\\left|\\phi\\right\\rangle$, respectively. Here, you should think of the pair $(i, j)$ as representing the bits of a single index $x \\in {0, 1, 2, 3}$. So for example, $(0, 0)$ is equivalent to index 0, (0, 1) to index 1, and (1, 1) to index 3. This implies that we can think of $\\left|\\psi\\right\\rangle\\otimes\\left|\\phi\\right\\rangle$ as having four entries, i.e. $\\left|\\psi\\right\\rangle\\otimes\\left|\\phi\\right\\rangle\\in \\mathbb{C}^4$ . Let us demonstrate with some examples:\n", "\n", "$$\n", "\\left|0\\right\\rangle\\otimes\\left|0\\right\\rangle= \\begin{pmatrix}1 \\\\ 0 \\end{pmatrix} \\otimes \\begin{pmatrix}1 \\\\ 0 \\end{pmatrix}=\\begin{pmatrix}1 \\\\ 0 \\\\ 0 \\\\ 0 \\end{pmatrix} \\qquad \\left|0\\right\\rangle\\otimes\\left|1\\right\\rangle= \\begin{pmatrix}1 \\\\ 0 \\end{pmatrix} \\otimes \\begin{pmatrix}0 \\\\ 1 \\end{pmatrix}=\\begin{pmatrix}0 \\\\ 1 \\\\0\\\\0\\end{pmatrix}\n", "$$\n", "\n", "#### Quantum Entanglement\n", "\n", "Now that we know how to stitch together a pair of single qubit states, it turns out we have opened Pandora’s box. For we can now talk about the two-qubit state which troubled Einstein to the end of his days — the innocuous-looking _Bell state_:\n", "\n", "$$\n", "\\left|\\Phi^+\\right\\rangle=\\frac{1}{\\sqrt 2}\\left|0\\right\\rangle\\left|0\\right\\rangle+\\frac{1}{\\sqrt 2}\\left|1\\right\\rangle\\left|1\\right\\rangle=\\begin{pmatrix}\\frac{1}{\\sqrt 2} \\\\ 0 \\\\0\\\\\\frac{1}{\\sqrt 2}\\end{pmatrix}\n", "$$\n", "This state demonstrates a quantum phenomenon known as _entanglement_ — intuitively, if a pair $q_0$ and $q_1$ of qubits are entangled, then they are so “tightly bound” that one cannot accurately describe the state of $q_0$ or $q_1$ alone — only the _joint_ state of $q_0$ and $q_1$ can be described precisely. In the language of tensor products, this is captured by the following statement: There do not exist $\\left|\\psi_1\\right\\rangle,\\left|\\psi_2\\right\\rangle\\in \\mathbb{C}^d$ such that $\\left|\\Phi^+\\right\\rangle=\\left|\\psi_1\\right\\rangle\\otimes\\left|\\psi_2\\right\\rangle$. In 1935, Einstein, Podolsky and Rosen published a famous paper nowadays referred to as the “EPR” paper, in which they argue that quantum mechanics cannot be a complete physical theory because it allows the existence of states such as $\\left|\\Phi^+\\right\\rangle$. Fast forwarding a number of decades, we now not only believe entanglement is real, but we know that is is _necessary resource_ for quantum computers to outperform classical ones.\n", "\n", "We shall later return to the topic of entanglement, but for now let us remark that there are three other such Bell states:\n", "\n", "$$\n", "\\begin{align}\n", "\\left|\\Phi^-\\right\\rangle&=\\frac{1}{\\sqrt 2}\\left|00\\right\\rangle-\\frac{1}{\\sqrt 2}\\left|11\\right\\rangle=\\begin{pmatrix}\\frac{1}{\\sqrt 2} \\\\ 0 \\\\0\\\\ -\\frac{1}{\\sqrt 2}\\end{pmatrix}\\\\\n", "\\left|\\Psi^+\\right\\rangle&=\\frac{1}{\\sqrt 2}\\left|01\\right\\rangle+\\frac{1}{\\sqrt 2}\\left|10\\right\\rangle=\\begin{pmatrix}0 \\\\ \\frac{1}{\\sqrt 2} \\\\\\frac{1}{\\sqrt 2}\\\\0\\end{pmatrix}\\\\\n", "\\left|\\Psi^-\\right\\rangle&=\\frac{1}{\\sqrt 2}\\left|01\\right\\rangle-\\frac{1}{\\sqrt 2}\\left|10\\right\\rangle=\\begin{pmatrix}0 \\\\ \\frac{1}{\\sqrt 2} \\\\-\\frac{1}{\\sqrt 2}\\\\0\\end{pmatrix}\\\\\n", "\\end{align}\n", "$$\n", "\n", "\n", "Note that here we have further simplified notation by letting (e.g.) $\\left|0\\right\\rangle\\left|0\\right\\rangle=\\left|00\\right\\rangle$. The four Bell states $\\left\\{\\left|\\Phi^+\\right\\rangle, \\left|\\Phi^-\\right\\rangle, \\left|\\Psi^+\\right\\rangle, \\left|\\Psi^-\\right\\rangle\\right\\}$ form an orthonormal basis for $\\mathbb{C}^{4}$ known as the Bell basis, after Northern Irish physicist John Bell.\n", "\n", "#### Two-qubit quantum gates.\n", "\n", "We have seen that two-qubit quantum states are described by unit vectors in $\\mathbb{C}^{4}$ . We can thus discuss two-qubit quantum gates, i.e. unitary operators $U \\in\\mathcal L (\\mathbb{C}^{4})$. There are two types of such gates: The first are simply tensor products of one-qubit gates, such as $X \\otimes Z$ or $H \\otimes H$. Here, the tensor product is defined analogously for matrices as it is for vectors. (The formal description is cumbersome, but we follow with a helpful illustration to clarify.) For any $A \\in\\mathcal L (\\mathbb{C}^{d_1})$,$B \\in\\mathcal L (\\mathbb{C}^{d_2})$ , $A \\otimes B$ is a $d_1d_2 \\times d_1d_2$ complex matrix whose entries are indexed by $([d_1] \\times [d_2], [d_1] \\times [d_2])$ (where $[d] = \\{0, . . . , d − 1\\}$ here), such that\n", "\n", "$$\n", "(A\\otimes B)((i_1,j_1),(i_2,j_2)):=A(i_1,i_2)B(j_1,j_2)\n", "$$\n", "\n", "To clarify this definition, suppose\n", "\n", "$$\n", "A=\n", "\\begin{pmatrix}\n", "a_1 & a_2 \\\\\n", "a_3 & a_4\n", "\\end{pmatrix}\n", "\\qquad\n", "B=\n", "\\begin{pmatrix}\n", "b_1 & b_2 \\\\\n", "b_3 & b_4\n", "\\end{pmatrix}\n", "$$\n", "\n", "Then $A\\otimes B$ is\n", "\n", "$$\n", "A \\otimes B =\n", "\\begin{pmatrix}\n", "a_1.\\begin{pmatrix}\n", "b_1 & b_2 \\\\\n", "b_3 & b_4\n", "\\end{pmatrix} & a_2 . \\begin{pmatrix}\n", "b_1 & b_2 \\\\\n", "b_3 & b_4\n", "\\end{pmatrix}\\\\\n", "a_3. \\begin{pmatrix}\n", "b_1 & b_2 \\\\\n", "b_3 & b_4\n", "\\end{pmatrix} & a_4. \\begin{pmatrix}\n", "b_1 & b_2 \\\\\n", "b_3 & b_4\n", "\\end{pmatrix}\n", "\\end{pmatrix}\n", "$$\n", "\n", "In other words, $A\\otimes B$ is obtained by taking four copies of $B$, each time multiplying by a different scalar entry of $A$.\n", "\n", "The tensor product for matrices shares the properties of the tensor product for vectors, with the addition of two rules below:\n", "\n", "$$\n", "\\begin{align*}\n", "(A \\otimes B)(C \\otimes D) &= AC \\otimes BD \\\\\n", "Tr(A \\otimes B) &= Tr(A)Tr(B).\n", "\\end{align*}\n", "$$\n", "\n", "In terms of circuit diagrams for tensor products of unitaries are like below: (We consider the cases of $X \\otimes I$, $I \\otimes Z$, and $H \\otimes H$, respectively.)\n", "\n", "![Some circuit examples](images/Lecture3-fig3-lr.png)\n", "\n", "Finally, we can also consider genuinely two-qubit gates, i.e. gates which are not the tensor product of single qubit gates. One important such gate is the controlled-NOT gate, denoted CNOT. The CNOT treats one qubit as the _control_ qubit, and the other as the target qubit. It then applies the Pauli $X$ gate to the target qubit only if the control qubit is set to $\\left|1\\right\\rangle$. More precisely, the action of the CNOT on a two-qubit basis is given as follows, where qubit 1 is the control and qubit 2 is the target\n", "\n", "$$\n", "\\text{CNOT}\\left|00\\right\\rangle=\\left|00\\right\\rangle \\qquad \\text{CNOT}\\left|01\\right\\rangle=\\left|01\\right\\rangle \\qquad \\text{CNOT}\\left|10\\right\\rangle=\\left|11\\right\\rangle \\qquad \\text{CNOT}\\left|11\\right\\rangle=\\left|10\\right\\rangle\n", "$$\n", "\n", "The CNOT gate is given by matrix:\n", "\n", "$$\n", "\\text{CNOT}=\n", "\\begin{pmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & 0 & 1 \\\\\n", "0 & 0 & 1 & 0\n", "\\end{pmatrix}\n", "=\\begin{pmatrix}\n", " I & 0 \\\\\n", "0 & X \\\\\n", "\\end{pmatrix}\n", "$$\n", "\n", "where the second expression is in block matrix form with $I$ and $X$ the identity and $X$ matrices.\n", "\n", "The circuit diagram for the CNOT is given by\n", "\n", "![CNOT](images/Lecture3-fig4-lr.png)\n", "\n", "With this in hand, we can do our first interesting computation — we can prepare the Bell state $\\Phi^+$ starting from an initial state of $\\left|00\\right\\rangle$ The preparation circuit is given as:\n", "\n", "![Entangler](images/Lecture3-fig5-lr.png)\n", "\n", "### Delayed choice quantum eraser\n", "\n", "A delayed-choice quantum eraser experiment, first performed by Yoon-Ho Kim, R. Yu, S. P. Kulik, Y. H. Shih and Marlan O. Scully, and reported in early 1999, is an elaboration on the quantum eraser experiment that incorporates concepts considered in Wheeler's delayed-choice experiment from late 70s to early 80s . The experiment was designed to investigate peculiar consequences of the well-known double-slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.\n", "\n", "\n", "![Delayed choice Quantum Eraser](images/Delayed-Choice-Quantum-Eraser-1.jpg)\n", "\n", "\n", " An argon laser generates individual 351.1 nm photons that pass through a double-slit apparatus (vertical black line in the upper left corner of the diagram).\n", "\n", "An individual photon goes through one (or both) of the two slits. In the illustration, the photon paths are color-coded as red or green lines to indicate which slit the photon came through (red indicates slit A, green indicates slit B).\n", "\n", "So far, the experiment is like a conventional two-slit experiment. However, after the slits, spontaneous parametric down-conversion (SPDC) is used to prepare an entangled two-photon state. This is done by a nonlinear optical crystal BBO (beta barium borate) that converts the photon (from either slit) into two identical, orthogonally polarized entangled photons with $\\frac{1}{2}$ the frequency of the original photon. The paths followed by these orthogonally polarized photons are caused to diverge by the Glan–Thompson prism.\n", "\n", "One of these 702.2 nm photons, referred to as the \"signal\" photon (look at the red and green lines going upwards from the Glan–Thompson prism) continues to the target detector called $D_0$. During an experiment, detector $D_0$ is scanned along its x axis, its motions controlled by a step motor. A plot of \"signal\" photon counts detected by $D_0$ versus x can be examined to discover whether the cumulative signal forms an interference pattern.\n", "\n", "The other entangled photon, referred to as the \"idler\" photon (look at the red and green lines going downwards from the Glan–Thompson prism), is deflected by prism PS that sends it along divergent paths depending on whether it came from slit A or slit B.\n", "\n", "Somewhat beyond the path split, the idler photons encounter beam splitters $S_a$, $S_b$, and $S_c$ that each have a 50% chance of allowing the idler photon to pass through and a 50% chance of causing it to be reflected. $M_a$ and $M_b$ are mirrors.\n", "\n", "The beam splitters and mirrors direct the idler photons towards detectors labeled $D_1$, $D_2$, $D_3$ and $D_4$. Note that:\n", "\n", "* If an idler photon is recorded at detector $D_3$, it can only have come from slit B.\n", "* If an idler photon is recorded at detector $D_4$, it can only have come from slit A.\n", "* If an idler photon is detected at detector $D_1$ or $D_2$, it might have come from slit A or slit B.\n", "* The optical path length measured from slit to $D_1$, $D_2$, $D_3$ and $D_4$ is 2.5 m longer than the optical path length from slit to $D_0$. This means that any information that one can learn from an idler photon must be approximately 8 ns later than what one can learn from its entangled signal photon.\n", "\n", "Let's call the green path $\\left|0\\right\\rangle$ and red path $\\left|1\\right\\rangle$. The double slit can be described by a Hadamard gate. The SPDC corresponds to a CNOT-gate. The state after the SPDC $\\frac{1}{2} \\left(\\left|00\\right\\rangle+\\left|11\\right\\rangle\\right)$. There is a phase $\\phi$ depending on the position $x$ of the detector $D_0$, which corresponds to a phase gate $R_\\phi$. The state before the measurement is\n", "\n", "$$\n", " \\frac{1}{2} \\left(\\left|00\\right\\rangle+\\left|10\\right\\rangle+e^{i\\phi}\\left|01\\right\\rangle-e^{i\\phi}\\left|11\\right\\rangle\\right)\n", " $$\n", " $$\n", " =\\frac{1}{2} \\left( \\left(\\left(1+e^{i\\phi}\\right)\\left|0\\right\\rangle+\\left(1-e^{i\\phi}\\right)\\left|1\\right\\rangle \\right)\\left|+\\right\\rangle+\\left(\\left(1-e^{i\\phi}\\right)\\left|0\\right\\rangle+\\left(1+e^{i\\phi}\\right)\\left|1\\right\\rangle \\right)\\left|-\\right\\rangle \\right)\n", " $$\n", "\n", "Detection of the idler photon by $D_3$ or $D_4$ provides delayed \"which-path information\" indicating whether the signal photon with which it is entangled had gone through slit A or B. On the other hand, detection of the idler photon by $D_1$ or $D_2$ provides a delayed indication that such information is not available for its entangled signal photon. Insofar as which-path information had earlier potentially been available from the idler photon, it is said that the information has been subjected to a \"delayed erasure\".\n", "\n", "* When the experimenters looked at the signal photons whose entangled idlers were detected at $D_1$ or $D_2$, they detected interference patterns.\n", "* However, when they looked at the signal photons whose entangled idlers were detected at $D_3$ or $D_4$, they detected simple diffraction patterns with no interference.\n", "\n", "\n", "Let's look at the probability to measure the a photon in $D_0$.\n", "\n", "* If we measure the second photon in $D_3$ or $D_4$, the post measurement state collapses to $\\left|\\pm\\right\\rangle$ basis. Then the probability for a click in $D_0$ is $\\frac{1}{2}$ . This is independent of the phase: no interference.\n", "* If we measure the second photon in $D_1$ or $D_2$, the probability for a click at $D_0$ is $\\frac{1}{2}\\left(1\\mp \\cos\\phi\\right)$, so here we see the interference. Whether we see interference or not depends on the basis choice on the second system, which can be delayed.\n", "\n", "![Oversimplified delayed choice quantum eraser](images/oversimplified_delayed_choice_eraser_quantum.png)\n", "\n", "![Simulated recordings](images/KimDelayedChoiceQuantumEraserGraphsGIF.gif)\n", "Simulated joint detection rates between $D_0$ and $D_1$, $D_2$, $D_3$, $D_4$ ($R_{01}$, $R_{02}$, $R_{03}$, $R_{04}$).\n", "\n", "\n", "\n", "![Quantum Eraser with coincidence counter](images/Kim_EtAl_Quantum_Eraser.svg.png)\n", "\n", "\n", "As you can see I have omitted the \"coincidence counter\" from the above description, similar to many people who talked about this experiment. Actually this is a key element. The coincidence counter would appear as a purely electronic device that acts on measurements. So if you would cast it as a quantum circuit it would look like this:\n", "\n", "![Coincidence counter Reveal case ](images/cycle-revealed.gif)\n", "![Coincidence counter Erasure case](images/cycle-erased.gif)\n", "\n", "The data was always the same! The \"erasure\" only changes how we *analyse* the data, i.e. what we keep and what we discard. This is done after the measurement, using an electronic circuit. There's no time travel, no disproof of materialism, just plain 'ol correlation being mistaken for causation.\n", "\n", "A full circuit can be found [here for reference purposes](https://algassert.com/quirk#circuit=%7B%22cols%22%3A%5B%5B1%2C%22H%22%5D%2C%5B1%2C%22%E2%80%A2%22%2C1%2C1%2C%22X%22%5D%2C%5B1%2C%22%7Eslits%22%2C%22QFT7%22%5D%2C%5B1%2C1%2C%22Measure%22%2C%22Measure%22%2C%22Measure%22%2C%22Measure%22%2C%22Measure%22%2C%22Measure%22%2C%22Measure%22%5D%2C%5B%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22Chance7%22%5D%2C%5B%22%E2%80%A6%22%2C%22%E2%80%A6%22%5D%2C%5B%22%E2%80%A6%22%2C%22%E2%80%A6%22%5D%2C%5B%22%E2%80%A6%22%2C%22%E2%80%A6%22%5D%2C%5B%22H%22%5D%2C%5B%22Measure%22%5D%2C%5B%22%7Echoice%22%5D%2C%5B%22%E2%80%A2%22%2C%22X%5E%C2%BD%22%5D%2C%5B1%2C%22Measure%22%5D%2C%5B1%2C%22%7Eresult%22%2C1%2C1%2C1%2C%22%7Eflat%22%5D%2C%5B%22%E2%97%A6%22%2C%22%E2%97%A6%22%2C%22Chance7%22%5D%2C%5B%22%E2%97%A6%22%2C%22%E2%80%A2%22%2C%22Chance7%22%5D%2C%5B1%2C1%2C1%2C1%2C1%2C%22%7Ewaves%22%5D%2C%5B%22%E2%80%A2%22%2C%22%E2%97%A6%22%2C%22Chance7%22%5D%2C%5B%22%E2%80%A2%22%2C%22%E2%80%A2%22%2C%22Chance7%22%5D%5D%2C%22gates%22%3A%5B%7B%22id%22%3A%22%7Echoice%22%2C%22name%22%3A%22choice%22%2C%22matrix%22%3A%22%7B%7B1%2C0%7D%2C%7B0%2C1%7D%7D%22%7D%2C%7B%22id%22%3A%22%7Eresult%22%2C%22name%22%3A%22result%22%2C%22matrix%22%3A%22%7B%7B1%2C0%7D%2C%7B0%2C1%7D%7D%22%7D%2C%7B%22id%22%3A%22%7Eflat%22%2C%22name%22%3A%22flat%22%2C%22matrix%22%3A%22%7B%7B1%2C0%7D%2C%7B0%2C1%7D%7D%22%7D%2C%7B%22id%22%3A%22%7Ewaves%22%2C%22name%22%3A%22waves%22%2C%22matrix%22%3A%22%7B%7B1%2C0%7D%2C%7B0%2C1%7D%7D%22%7D%2C%7B%22id%22%3A%22%7Eslits%22%2C%22name%22%3A%22slits%22%2C%22matrix%22%3A%22%7B%7B1%2C0%7D%2C%7B0%2C1%7D%7D%22%7D%5D%7D)\n", "\n", "In fact you can even make classical analogues:\n", "Bob has a six-sided die, a two-sided coin, and a small empty box to put the coin in. He rolls the die, gets a result between 1 and 6, and places the coin in the box in a way that depends on the die roll. If the die roll was even, the coin is placed heads up. If the die roll was odd, the coin is placed tails up. Bob then writes down his die roll, and carefully hands the box to Alice.\n", "\n", "Alice now has to decide to either a) just open the box or b) shake the box before opening it. (Shaking the box randomizes the coin.) Once the box is open, she writes down whether the coin was face up or face down, and also writes down whether or not she shook the box.\n", "\n", "![Classical erasure](images/classical-banded-choice.png)\n", "\n", "The tweaked delayed choice quantum eraser so that there isn't a classical analogue is called a [Bell test](https://en.wikipedia.org/wiki/Bell_test), however it lacks the \"characteristics\" of the delayed choice quantum eraser. For example, in order to avoid the signalling loophole, the choice can no longer be delayed.\n", "\n", "### Postulate 4: Measurement\n", "\n", "How do we mathematically model the act of measuring or observing a quantum system considering that the very act of looking at or observing a quantum system irreversibly alters the state of the system? To model this phenomenon, we shall use the notion of a projective or von Neumann measurement (named after Hungarian child prodigy and mathematician, John von Neumann, who was apparently already familiar with calculus at the age of 8). To do so, we must define three classes of linear operators, each of which is increasingly more restricted. All three classes will prove vital throughout this course.\n", "\n", " 1. *Hermitian operators*: An operator $M \\in \\mathcal L \\left(\\mathbb C^d \\right)$ is Hermitian if $M = M^\\dagger$ . Examples you are already familiar with are the Pauli $X$, $Y$ , and $Z$ gates, which are not only unitary, but also Hermitian. A Hermitian operator has the important property that all of its eigenvalues are real. Thus, Hermitian operators can be thought of as a higher dimensional generalization of the real numbers.\n", " 2. *Positive semi-definite operators*: If a Hermitian operator has only non-negative eigenvalues, then it is called positive-semidefinite. Thus, positive semi-definite (or positive for short) matrices generalize the non-negative real numbers.\n", " 3. *Orthogonal projection operators*: A Hermitian matrix $\\Pi \\in \\mathcal L \\left(\\mathbb C^d \\right)$ is an orthogonal projection operator (or projector for short) if $\\Pi^2=\\Pi$. This is equivalent to saying $\\Pi$ has only eigenvalues 0 and 1. Let us prove this equivalence briefly: Since $\\Pi$ is Hermitian, we can take its spectral decomposition, $\\Pi = \\sum_i \\lambda_i \\left|\\lambda_i\\right\\rangle\\left\\langle\\lambda_i\\right|$. Hence,\n", " $$\n", " \\sum_i \\lambda_i \\left|\\lambda_i\\right\\rangle\\left\\langle\\lambda_i\\right|=\\Pi =\\Pi^2=\\left(\\sum_i \\lambda_i \\left|\\lambda_i\\right\\rangle\\left\\langle\\lambda_i\\right|\\right)\\left(\\sum_i \\lambda_i \\left|\\lambda_i\\right\\rangle\\left\\langle\\lambda_i\\right|\\right)=\\sum_i \\lambda_i^2 \\left|\\lambda_i\\right\\rangle\\left\\langle\\lambda_i\\right|\n", " $$\n", " where the last equality follows since {|λi i} is an orthonormal basis. Since the |λi i are orthogonal, we thus have that for all i, λi = λ2i . But this can only hold if λi ∈ {0, 1}, as claimed.\n", "\n", " It is important to note that since a projector $\\Pi$’s eigenvalues are all 0 or 1, its spectral decomposition must take the form $\\Pi=\\sum_i \\left|\\psi_i\\right\\rangle\\left\\langle\\psi_i\\right|$, where $\\left\\{\\left|\\psi_i\\right\\rangle\\right\\}$ are an orthonormal set. Conversely, summing any set of orthonormal $\\left\\{\\left|\\psi_i\\right\\rangle\\right\\}$ in this fashion yields projector. Observe that a projector $\\Pi$ has rank 1 if and only if $\\Pi=\\left|\\psi\\right\\rangle\\left\\langle\\psi\\right|$ for some $\\left|\\psi_i\\right\\rangle \\in \\mathbb C ^ d $ , since the rank of $\\Pi$ equals the number of non-zero eigenvalues of $\\Pi$, and here $\\Pi=\\left|\\psi\\right\\rangle\\left\\langle\\psi\\right|$ is a spectral decomposition of $\\Pi$. Finally,let us develop an intuition for what a projector actually *does* — for any projector $\\Pi=\\sum_i \\left|\\psi_i\\right\\rangle\\left\\langle\\psi_i\\right|$ and state $\\left|\\phi\\right\\rangle$ to be measured, we have\n", " $$\n", " \\Pi\\left|\\phi\\right\\rangle=\\left(\\sum_i \\left|\\psi_i\\right\\rangle\\left\\langle\\psi_i\\right|\\right)\\left|\\phi\\right\\rangle=\\sum_i \\left|\\psi_i\\right\\rangle\\left(\\left\\langle\\psi_i\\middle|\\phi\\right\\rangle\\right)=\\sum_i \\left(\\left\\langle\\psi_i\\middle|\\phi\\right\\rangle\\right)\\left|\\psi_i\\right\\rangle\\in\\text{Span}\\left\\{\\left|\\psi_i\\right\\rangle\\right\\}\n", " $$\n", "\n", " where note $\\left\\langle\\psi_i\\middle|\\phi\\right\\rangle\\in \\mathbb C$. Thus, $\\Pi$ projects us down onto the span of the vectors $\\left\\{\\left|\\psi_i\\right\\rangle\\right\\}$.\n", "\n", "### Projective Measurements.\n", "\n", "With projectors in hand, we can now define a projective measurement. A *projective measurement* is a set of projectors $B = \\left\\{\\Pi_i\\right\\}_{i=0}^m$ such that $\\sum_{i=0}^m \\Pi_i = I$. The latter condition is called the completeness relation. If each $\\Pi_i$ is rank one, i.e. $\\Pi_i=\\left|\\psi_i\\right\\rangle\\left\\langle\\psi_i\\right|$, then we say that $B$ models a *measurement in basis* $\\left\\{\\left|\\psi_i\\right\\rangle\\right\\}$. Often, we shall measure in the computational basis, which is specified by $B= \\left\\{\\left|0\\right\\rangle\\left\\langle0\\right|,\\left|1\\right\\rangle\\left\\langle1\\right|\\right\\}$ in the case of $\\mathbb C ^ 2$ (and generalizes as $B= \\left\\{\\left|i\\right\\rangle\\left\\langle,\\right|\\right\\}_{i=0}^{d-1}$ for $\\mathbb C^d$)\n", "\n", "With a projective measurement $B = \\left\\{\\Pi_i\\right\\}_{i=0}^m\\subseteq\\mathbb C^d$ in hand, let us *specify* how one uses $B$. Suppose our quantum system is in state $\\left|\\psi\\right\\rangle\\in\\mathbb C^d$ . Then, the probability of obtaining outcome $i \\in \\{0, . . . , m\\}$ when measuring $\\left|\\psi\\right\\rangle$ with $B$ is given by\n", "$$\n", "\\text{Pr}(\\text{outcome } i) = \\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i \\right) = \\text{Tr}\\left(\\Pi_i^2 \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\right) = \\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\right),\n", "$$\n", "where the second equality follows by the cyclic property of the trace and the third since $\\Pi_i$ is\n", "a projector.\n", "\n", "The exercise above has an important moral — requiring a quantum state $\\left|\\psi\\right\\rangle$ to be a unit vector (i.e. $\\left|\\alpha\\right|^2 + \\left|\\beta\\right|^2 = 1$) ensures that when measuring $\\left|\\psi\\right\\rangle$, the distribution over the outcomes is a valid probability distribution, i.e. the probabilities for all possible outcomes sum to 1. The other important take-home message here is that measurements in quantum mechanics are inherently probabilistic — in general, the outcomes cannot be perfectly predicted! Finally, we started this lecture by saying that the very act of measuring a quantum state disturbs the system. Let us now formalize this; we will crucially use the fact discussed earlier that a projector projects a vector $\\left|\\psi\\right\\rangle$ down into a smaller subspace. Specifically, upon obtaining outcome $\\Pi_i$ when measuring $B$, the state of system “collapses” to\n", "\n", "$$\n", "\\frac{\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i }{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i \\right)}=\\frac{\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i }{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right| \\right)}\n", "$$\n", "\n", "Note the denominator above is a scalar, and is just the probability of outcome $i$. There are two points here which may confuse you: Why have we written the output state as a matrix $\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i$ rather than a vector $\\Pi_i \\left|\\psi\\right\\rangle$, and what is the role of the denominator? Let us handle each of these in order.\n", "\n", "First, conditioned on outcome $\\Pi_i$ , the output state is indeed a vector, namely $\\Pi_i \\left|\\psi\\right\\rangle$. However, there is a more general formalism which we shall discuss shortly called the *density operator formalism*, in which quantum states are written as matrices, not vectors. Specifically, the “density matrix” representing vector $\\left|\\psi\\right\\rangle$ would be written as matrix $\\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|$. The density operator formalism is more general than the state vector approach we have taken so far, and will be crucial for studying individual subsystems of a larger composite quantum state. Thus, the answer to question 1 is that we have written the output as a matrix simply to slowly ease the transition into the density matrix formalism.\n", "\n", "The motive behind question 2 is somewhat less sinister — the problem here is that since we projected out part of $\\left|\\psi\\right\\rangle$ during the measurement, the output $\\Pi_i \\left|\\psi\\right\\rangle$ may not necessarily be normalized. To renormalize $\\Pi_i \\left|\\psi\\right\\rangle$, we simply divide by its Euclidean norm to obtain\n", "\n", "$$\n", "\\left|\\psi^\\prime\\right\\rangle=\\frac{\\Pi_i \\left|\\psi\\right\\rangle}{\\left\\|\\Pi_i \\left|\\psi\\right\\rangle\\right\\|_2}=\\frac{\\Pi_i \\left|\\psi\\right\\rangle}{\\sqrt{ \\left\\langle\\psi\\right| \\Pi_i \\Pi_i \\left|\\psi\\right\\rangle}}=\\frac{\\Pi_i \\left|\\psi\\right\\rangle}{\\sqrt{ \\left\\langle\\psi\\right| \\Pi_i \\left|\\psi\\right\\rangle}}\n", "$$\n", "\n", "The state $\\left|\\psi^\\prime\\right\\rangle$ describes the post-measurement state of our system, assuming we have obtained outcome $i$.\n", "\n", "A final quirk we should iron out is the following — in terms of measurements, what is the consequence of the fact that a projector $\\Pi_i$ satisfies $\\Pi_i^2 = \\Pi_i$ ? Well, if you observe a quantum system now, and then again five minutes from now, and if the system has not been subjected to any gates or noise in between the measurements, then the two measurement results you obtain should agree (I realize the study of quantum mechanics has likely distorted your view of when you can trust your intuition, but this is one case in which you can). To model this, suppose we measure using $B = \\{\\Pi_i\\}$ and obtain results $i$ and $j$ in measurements 1 and 2, respectively. Then:\n", "\n", "$$\n", "\\text{Pr}\\left(\\text{outcome } i \\middle| \\text{outcome } j\\right)=\\text{Tr}\\left(\\Pi_j\\frac{\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i }{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right| \\right)}\\Pi_j\\right)=\\frac{\\text{Tr}\\left(\\Pi_j\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i\\Pi_j \\right)}{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right| \\right)}\n", "$$\n", "\n", "To simplify this expression, we use the fact that if the completeness relation holds for projectors $\\{\\Pi_i\\}$, i.e. $\\sum_i \\Pi_i = I$, then it turns out that $\\Pi_j \\Pi_1 = \\delta_{ij} \\Pi_i$, where recall $\\delta_ij$ is the Kronecker delta. Thus, if $i\\neq j$, above equation equals to 0, and if $i = j$, it reduces to\n", "$$\n", "\\frac{\\text{Tr}\\Pi_j\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i\\Pi_j }{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right| \\right)}=\\frac{\\text{Tr}\\left(\\Pi_i^2 \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i^2 \\right)}{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right| \\right)}=\\frac{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\Pi_i\\right) }{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right| \\right)}=\\frac{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|\\right)}{\\text{Tr}\\left(\\Pi_i \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right| \\right)}=1\n", "$$\n", "i.e. measuring the state a second time again yields outcome i with probability 1, as desired.\n", "Thus, although observing a state for the first time disturbs it, subsequent measurements will\n", "consistently return the same measurement result!\n", "\n", "We close this section by giving the circuit symbol which denotes a measurement of a qubit $\\left|\\psi\\right\\rangle \\in \\mathbb C^2$ in the computational basis $B= \\left\\{\\left|0\\right\\rangle\\left\\langle0\\right|,\\left|1\\right\\rangle\\left\\langle1\\right|\\right\\}$:\n", "\n", "![Measurement circuit](images/measure_circuit.png)\n", "\n", "The double-wires on the right side indicate that the output of the measurement is a classical string (indicating which measurement outcome was obtained).\n", "\n", "## Quantum Teleportation\n", "\n", "With the concepts of the Bell state and measurement in hand, we can discuss our first neat computational trick: Quantum teleportation. Suppose you have a single-qubit quantum state $\\left|\\psi\\right\\rangle= \\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle $ in your possession (i.e. as a physical system, not on paper), but that you do not know the values of $\\alpha$ and $\\beta$. Your friend Alice now phones you and asks to borrow your state. How can you send it to her? One obvious way is simply to pop your system in the mail and physically send it over. However, it turns out that by exploiting the phenomenon of entanglement, you can do something incredible — by sending two classical bits over the telephone to Alice, you can “teleport” $\\left|\\psi\\right\\rangle$ instantly to her!\n", "\n", "To teleport $\\left|\\psi\\right\\rangle$, we assume that you and Alice each share half of a Bell state $\\left|\\Phi^+\\right\\rangle=\\frac{1}{\\sqrt 2}\\left(\\left|00\\right\\rangle+\\left|11\\right\\rangle\\right)$ to begin with; specifically, you hold qubit 1 of $\\left|\\Phi^+\\right\\rangle$, and Alice holds qubit 2. The teleportation circuit is then given as follows:\n", "\n", "![The teleportation circuit](images/teleportation_circuit.png)\n", "\n", "Let us break this down piece by piece. The first two wires are held by you; wire 1 holds the state to be teleported, $\\left|\\psi\\right\\rangle$, and wire 2 holds your half of $\\left|\\Phi^+\\right\\rangle$. The third wire holds Alice’s half of $\\left|\\Phi^+\\right\\rangle$. Note that we have used $\\left|\\Phi^+_A\\right\\rangle$ and $\\left|\\Phi^+_B\\right\\rangle$ to denote the two “halves” of $\\left|\\Phi^+\\right\\rangle$, but this is poor notation — read literally, this diagram suggests $\\left|\\Phi^+\\right\\rangle=\\left|\\Phi^+_A\\right\\rangle\\otimes\\left|\\Phi^+_B\\right\\rangle$, which is not true since is $\\left|\\Phi^+\\right\\rangle$ entangled, and hence from last lecture we know that there do not exist states $\\left|\\Phi^+_A\\right\\rangle$ and $\\left|\\Phi^+_B\\right\\rangle$ such that $\\left|\\Phi^+\\right\\rangle=\\left|\\Phi^+_A\\right\\rangle\\otimes\\left|\\Phi^+_B\\right\\rangle$ This notation is for illustration purposes only, not to complicate the diagram, and make our analysis easy.\n", "\n", "The circuit can be divided into 5 steps: Step 1 performs the CNOT, Step 2 the Hadamard gate, Step 3 measures qubits 1 and 2, Step 4 applies a conditional X gate, and Step 5 applies a conditional Z gate. The latter two require clarification: The conditional X gate here takes a classical bit $b$ as input (hence the incoming wire at the top is a double line), and applies X if and only if $b = 1$. The conditional Z gate is defined analogously.\n", "\n", "Now that we have technically parsed this diagram, let us intuitively parse it. First, you begin in Steps 1 and 2 by performing a CNOT and Hadamard on your qubits, followed by a standard basis measurement in Step 3. Since a measurement in the standard basis maps each qubit to either $\\left|0\\right\\rangle$ or $\\left|1\\right\\rangle$, the output of your two measurements can jointly be thought of as one of the four bit strings $00$, $01$, $10$, or $11$. Call these bits $b_0 b_1$ . Now you pick up the telephone, call Alice, and tell her the value of $b_0 b_1$ . Conditioned on $b_0 $ , she applies X to her half of the Bell pair, followed by Z conditioned on $b_1$. The claim is that at this point, Alice’s qubit’s state has been magically converted to $\\left|\\psi\\right\\rangle$. In fact, as we shall see shortly, $\\left|\\psi\\right\\rangle$ has also disappeared from your possession! In this sense, teleportation has taken place.\n", "\n", "Let us formally analyze the action of this circuit. Denote by $\\left|\\psi_1\\right\\rangle$ for $i \\in \\{0, . . . , 5\\}$ the joint state of your and Alice’s systems immediately after Step $i$ has taken place. Here, we define $\\left|\\psi_0\\right\\rangle$ as the initial joint state before any gates are applied; it is given by\n", "\n", "$$\n", "\\begin{align}\n", "\\left|\\psi_0\\right\\rangle=\\left|\\psi\\right\\rangle\\left|\\Phi^+\\right\\rangle=\\left(\\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle\\right)\\left(\\frac{1}{\\sqrt 2}\\left|00\\right\\rangle+\\frac{1}{\\sqrt 2}\\left|11\\right\\rangle\\right)=\\frac{1}{\\sqrt 2}\\left(\\alpha\\left|000\\right\\rangle+\\alpha\\left|011\\right\\rangle+\\beta\\left|100\\right\\rangle+\\beta\\left|111\\right\\rangle\\right)\n", "\\end{align}\n", "$$\n", "\n", "After Step 1, i.e. after the CNOT, we have state\n", "\n", "$$\n", "\\frac{1}{\\sqrt 2}\\left(\\alpha\\left|000\\right\\rangle+\\alpha\\left|011\\right\\rangle+\\beta\\left|110\\right\\rangle+\\beta\\left|101\\right\\rangle\\right)\n", "$$\n", "\n", "After Step 2, i.e. after the Hadamard gate, we have\n", "\n", "$$\n", "\\begin{align}\n", "&\\frac{1}{\\sqrt 2}\\left(\\alpha\\left|+\\right\\rangle\\left|00\\right\\rangle+\\alpha\\left|+\\right\\rangle\\left|11\\right\\rangle+\\beta\\left|-\\right\\rangle\\left|10\\right\\rangle+\\beta\\left|-\\right\\rangle\\left|01\\right\\rangle\\right)\\\\\n", "&=\\frac{1}{2}\\left(\\alpha(\\left|0\\right\\rangle+\\left|1\\right\\rangle)\\left|00\\right\\rangle+\\alpha(\\left|0\\right\\rangle+\\left|1\\right\\rangle)\\left|11\\right\\rangle+\\beta(\\left|0\\right\\rangle-\\left|1\\right\\rangle)\\left|10\\right\\rangle+\\beta(\\left|0\\right\\rangle-\\left|1\\right\\rangle)\\left|01\\right\\rangle\\right)\\\\\n", "&=\\frac{1}{2}\\left(\\left|00\\right\\rangle\\left(\\alpha\\left|0\\right\\rangle+\\beta\\left|1\\right\\rangle\\right)+\\left|01\\right\\rangle\\left(\\alpha\\left|0\\right\\rangle+\\beta\\left|1\\right\\rangle\\right)+\\left|10\\right\\rangle\\left(\\alpha\\left|0\\right\\rangle-\\beta\\left|1\\right\\rangle\\right)+\\left|11\\right\\rangle\\left(\\alpha(\\left|1\\right\\rangle-\\beta\\left|0\\right\\rangle\\right)\\right)\n", "\\end{align}\n", "$$\n", "\n", "Let us now pause and analyze the state of affairs. There are four terms in this superposition, each of which begins with a distinct bit string $\\left|00\\right\\rangle$, $\\left|01\\right\\rangle$, $\\left|10\\right\\rangle$, or $\\left|11\\right\\rangle$. This means that if you now measure qubits 1 and 2 in the standard basis and obtain outcome (say) $\\left|00\\right\\rangle$, then Alice’s qubit on wire 3 collapses to the only consistent possibility, $\\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle$. In this case, teleportation has already taken place.\n", "\n", "More generally, the four possible outcomes upon measuring qubits 1 and 2 result in four distinct residual states on Alice’s qubit as follows:\n", "$$\n", "00\\rightarrow\\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle\\qquad 01\\rightarrow\\alpha\\left|1\\right\\rangle + \\beta\\left|0\\right\\rangle\\qquad 10\\rightarrow\\alpha\\left|0\\right\\rangle - \\beta\\left|1\\right\\rangle\\qquad 11\\rightarrow\\alpha\\left|1\\right\\rangle - \\beta\\left|0\\right\\rangle\n", "$$\n", "\n", "Thus, if you simply send the two bits $b_0 b_1$ encoding the measurement outcome to Alice, then regardless of the value of $b_0 b_1$ , she can recover your original state $\\left|\\psi\\right\\rangle=\\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle $ via the following identities:\n", "\n", "$$\n", "X\\left(\\alpha\\left|1\\right\\rangle + \\beta\\left|0\\right\\rangle\\right)=\\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle \\qquad Z\\left(\\alpha\\left|0\\right\\rangle - \\beta\\left|1\\right\\rangle\\right)=\\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle \\qquad\n", "ZX\\left(\\alpha\\left|1\\right\\rangle - \\beta\\left|0\\right\\rangle\\right)=\\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle\n", "$$\n", "\n", "In other words, by conditionally applying X and Z based on the outputs $b_0 b_1$ from your measurement, Alice can successfully recover your state $\\left|\\psi\\right\\rangle=\\alpha\\left|0\\right\\rangle + \\beta\\left|1\\right\\rangle $ . This is precisely what is depicted in Steps 4 and 5 of the teleportation circuit. Finally, note that since measuring your qubits leaves you in one of the four standard basis states $\\left|00\\right\\rangle$, $\\left|01\\right\\rangle$, $\\left|10\\right\\rangle$, or $\\left|11\\right\\rangle$ the state $\\left|\\psi\\right\\rangle$ has now “disappeared” from your possession!" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Preliminary\n", "\n", "First of all, let's see if your qiskit installation is working. If not, please follow the instructions for installing qiskit in your own pc using _conda_, or run this book in the _IBM cloud_ directly." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.19.2
qiskit-aer0.10.3
qiskit-ignis0.7.0
qiskit-ibmq-provider0.18.3
qiskit0.34.2
qiskit-nature0.3.1
qiskit-optimization0.3.1
qiskit-machine-learning0.3.1
System information
Python version3.8.12
Python compilerGCC 7.5.0
Python builddefault, Oct 12 2021 13:49:34
OSLinux
CPUs24
Memory (Gb)62.71327590942383
Thu Mar 17 17:01:22 2022 +03
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Exploring Qubits with Qiskit\n", "\n", "Classical bits always have a completely well-defined state: they are either 0 or 1 at every point during a computation. There is no more detail we can add to the state of a bit than this. So to write down the state of a of classical bit `(c)`, we can just use these two binary values. For example:\n", "\n", "$$\n", "c = 0\n", "$$\n", "\n", "This restriction is lifted for quantum bits. Whether we get a $0$ or a $1$ from a qubit only needs to be well-defined when a measurement is made to extract an output. At that point, it must commit to one of these two options. At all other times, its state will be something more complex than can be captured by a simple binary value.\n", "\n", "To see how to describe these, we can first focus on the two simplest cases. It is possible to prepare a qubit in a state for which it definitely gives the outcome $0$ when measured.\n", "\n", "We need a name for this state. Let's be unimaginative and call it *0*. Similarly, there exists a qubit state that is certain to output a $1$. We'll call this *1*. These two states are completely mutually exclusive. Either the qubit definitely outputs a $0$, or it definitely outputs a $1$. There is no overlap. One way to represent this with mathematics is to use two orthogonal vectors.\n", "\n", "$$\n", "\\left|0\\right\\rangle= \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix} \\qquad \\left|1\\right\\rangle= \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}\n", "$$\n", "\n", "With vectors we can describe more complex states than just $\\left|0\\right\\rangle$ and $\\left|1\\right\\rangle$. For example, consider the vector\n", "\n", "$$\n", "\\left|q_0\\right\\rangle= \\begin{pmatrix} \\frac{1}{\\sqrt{2}} \\\\ \\frac{i}{\\sqrt{2}} \\end{pmatrix}\n", "$$\n", "\n", "Since the states $\\left|0\\right\\rangle$ and $\\left|1\\right\\rangle$ form an orthonormal basis, we can represent any 2D vector with a combination of these two states. This allows us to write the state of our qubit in the alternative form:\n", "\n", "$$\n", "\\left|q_0\\right\\rangle = \\frac{1}{\\sqrt{2}} \\left|0\\right\\rangle + \\frac{i}{\\sqrt{2}} \\left|1\\right\\rangle\n", "$$\n", "\n", "This vector, $\\left|q_0\\right\\rangle$ is called the qubit's _statevector_, it tells us everything we could possibly know about this qubit. For now, we are only able to draw a few simple conclusions about this particular example of a statevector: it is not entirely $\\left|0\\right\\rangle$ and not entirely $\\left|1\\right\\rangle$. Instead, it is described by a linear combination of the two. In quantum mechanics, we typically describe linear combinations such as this using the word 'superposition'.\n", "\n", "Though our example state $\\left|q_0\\right\\rangle$ can be expressed as a superposition of $\\left|0\\right\\rangle$ and $\\left|1\\right\\rangle$, it is no less a definite and well-defined qubit state than they are. To see this, we can begin to explore how a qubit can be manipulated" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "First, we need to import all the tools we will need:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from qiskit import QuantumCircuit, assemble, Aer\n", "from qiskit.visualization import plot_histogram, plot_bloch_vector\n", "from math import sqrt, pi" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "In Qiskit, we use the `QuantumCircuit` object to store our circuits, this is essentially a list of the quantum operations on our circuit and the qubits they are applied to." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "qc = QuantumCircuit(1) # Create a quantum circuit with one qubit" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "In our quantum circuits, our qubits always start out in the state $\\left|q_0\\right\\rangle$. We can use the `initialize()` method to transform this into any state. We give `initialize()` the vector we want in the form of a list, and tell it which qubit(s) we want to initialize in this state:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1) # Create a quantum circuit with one qubit\n", "initial_state = [0,1] # Define initial_state as |1>\n", "qc.initialize(initial_state, 0) # Apply initialisation operation to the 0th qubit\n", "qc.draw('mpl') # Let's view our circuit" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "We can then use one of Qiskit’s simulators to view the resulting state of our qubit." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sim = Aer.get_backend('aer_simulator') # Tell Qiskit how to simulate our circuit" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "To get the results from our circuit, we use run to execute our circuit, giving the circuit and the backend as arguments. We then use `.result()` to get the result of this:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "qc = QuantumCircuit(1) # Create a quantum circuit with one qubit\n", "initial_state = [0,1] # Define initial_state as |1>\n", "qc.initialize(initial_state, 0) # Apply initialisation operation to the 0th qubit\n", "qc.save_statevector() # Tell simulator to save statevector\n", "qobj = assemble(qc) # Create a Qobj from the circuit for the simulator to run\n", "result = sim.run(qobj).result() # Do the simulation and return the result" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "from result, we can then get the final statevector using `.get_statevector()`:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Statevector([0.+0.j, 1.+0.j],\n", " dims=(2,))\n" ] } ], "source": [ "out_state = result.get_statevector()\n", "print(out_state) # Display the output state vector" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "*Note:* Python uses $j$ to represent $i$ in complex numbers. We see a vector with two complex elements: $0.+0.j = 0$, and $1.+0.j = 1$.\n", "\n", "Let’s now measure our qubit as we would in a real quantum computer and see the result:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc.measure_all()\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "This time, instead of the statevector we will get the counts for the $0$ and $1$ results using `.get_counts()`:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qobj = assemble(qc)\n", "result = sim.run(qobj).result()\n", "counts = result.get_counts()\n", "plot_histogram(counts)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "We can see that we (unsurprisingly) have a 100% chance of measuring $\\left|1\\right\\rangle$. This time, let’s instead put our qubit into a superposition and see what happens. We will use the state $\\left|q_0\\right\\rangle$ from earlier :\n", "\n", "$$\n", "\\left|q_0\\right\\rangle = \\frac{1}{\\sqrt{2}} \\left|0\\right\\rangle + \\frac{i}{\\sqrt{2}} \\left|1\\right\\rangle\n", "$$\n", "\n", "We need to add these amplitudes to a python list. To add a complex amplitude, Python uses $j$ for the imaginary unit (we normally call it $i$ mathematically):" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "initial_state = [1/sqrt(2), 1j/sqrt(2)] # Define state |q_0>" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "And we then repeat the steps for initialising the qubit as before:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Statevector([0.70710678+0.j , 0. +0.70710678j],\n", " dims=(2,))\n" ] } ], "source": [ "qc = QuantumCircuit(1) # Must redefine qc\n", "qc.initialize(initial_state, 0) # Initialize the 0th qubit in the state `initial_state`\n", "qc.save_statevector() # Save statevector\n", "qobj = assemble(qc)\n", "state = sim.run(qobj).result().get_statevector() # Execute the circuit\n", "print(state) # Print the result" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qobj = assemble(qc)\n", "results = sim.run(qobj).result().get_counts()\n", "plot_histogram(results)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "We can see we have equal probability of measuring either $\\left|0\\right\\rangle$ or $\\left|1\\right\\rangle$. To explain this, we need to talk about measurement." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## The Rules of Measurement\n", "\n", "Remember: To find the probability of measuring a state $\\left|\\psi\\right\\rangle$ in the state $\\left|x\\right\\rangle$ we do:\n", "\n", "$$\n", "p\\left(\\left|x\\right\\rangle\\right)=\\left|\\left\\langle x\\middle|\\psi\\right\\rangle\\right|^2\n", "$$\n", "\n", "In the equation above, $\\left|x\\right\\rangle$ can be any qubit state. To find the probability of measuring $\\left|x\\right\\rangle$, we take the inner product of $\\left|x\\right\\rangle$ and the state we are measuring (in this case $\\left|\\psi\\right\\rangle$), then square the magnitude. This may seem a little convoluted, but it will soon become second nature.\n", "\n", "If we look at the state $\\left|q_0\\right\\rangle$ from before, we can see the probability of measuring $\\left|0\\right\\rangle$ is indeed $0.5$ :\n", "\n", "$$\n", "\\begin{aligned}\n", "\\left|q_0\\right\\rangle &= \\frac{1}{\\sqrt{2}} \\left|0\\right\\rangle + \\frac{i}{\\sqrt{2}} \\left|1\\right\\rangle \\\\\n", "\\left\\langle 0 \\middle|q_0\\right\\rangle &= \\frac{1}{\\sqrt{2}} \\left\\langle 0 \\middle|0\\right\\rangle + \\frac{i}{\\sqrt{2}} \\left\\langle 0 \\middle|1\\right\\rangle \\\\\n", ".&=\\frac{1}{\\sqrt{2}}\\\\\n", "\\left|\\left\\langle 0 \\middle|q_0\\right\\rangle\\right|^2 &=\\frac{1}{2}\n", "\\end{aligned}\n", "$$\n", "\n", "This rule governs how we get information out of quantum states. It is therefore very important for everything we do in quantum computation. It also immediately implies several important facts" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### Normalisation\n", "\n", "The rule shows us that amplitudes are related to probabilities. If we want the probabilities to add up to 1 (which they should!), we need to ensure that the statevector is properly normalized. Specifically, we need the magnitude of the state vector to be 1.\n", "\n", "$$\n", "\\left\\langle \\psi \\middle|\\psi\\right\\rangle=1\n", "$$\n", "\n", "Thus if:\n", "\n", "$$\n", "\\left|\\psi\\right\\rangle = \\alpha \\left|0\\right\\rangle + \\beta \\left|1\\right\\rangle\n", "$$\n", "\n", "Then:\n", "\n", "$$\n", "\\left|\\alpha\\right|^2+\\left|\\beta\\right|^2=1\n", "$$\n", "\n", "This explains the factors of $\\sqrt{2}$ you have seen throughout this hands-on. In fact, if we try to give `initialize()` a vector that isn’t normalised, it will give us an error:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "ename": "QiskitError", "evalue": "'Sum of amplitudes-squared does not equal one.'", "output_type": "error", "traceback": [ "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", "\u001B[0;31mQiskitError\u001B[0m Traceback (most recent call last)", "Input \u001B[0;32mIn [14]\u001B[0m, in \u001B[0;36m\u001B[0;34m()\u001B[0m\n\u001B[1;32m 1\u001B[0m vector \u001B[38;5;241m=\u001B[39m [\u001B[38;5;241m1\u001B[39m,\u001B[38;5;241m1\u001B[39m]\n\u001B[0;32m----> 2\u001B[0m \u001B[43mqc\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43minitialize\u001B[49m\u001B[43m(\u001B[49m\u001B[43mvector\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m0\u001B[39;49m\u001B[43m)\u001B[49m\n", "File \u001B[0;32m~/Prog/miniconda3/envs/qiskit/lib/python3.8/site-packages/qiskit/extensions/quantum_initializer/initializer.py:459\u001B[0m, in \u001B[0;36minitialize\u001B[0;34m(self, params, qubits)\u001B[0m\n\u001B[1;32m 456\u001B[0m qubits \u001B[38;5;241m=\u001B[39m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39m_bit_argument_conversion(qubits, \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mqubits)\n\u001B[1;32m 458\u001B[0m num_qubits \u001B[38;5;241m=\u001B[39m \u001B[38;5;28;01mNone\u001B[39;00m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m \u001B[38;5;28misinstance\u001B[39m(params, \u001B[38;5;28mint\u001B[39m) \u001B[38;5;28;01melse\u001B[39;00m \u001B[38;5;28mlen\u001B[39m(qubits)\n\u001B[0;32m--> 459\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mappend(\u001B[43mInitialize\u001B[49m\u001B[43m(\u001B[49m\u001B[43mparams\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mnum_qubits\u001B[49m\u001B[43m)\u001B[49m, qubits)\n", "File \u001B[0;32m~/Prog/miniconda3/envs/qiskit/lib/python3.8/site-packages/qiskit/extensions/quantum_initializer/initializer.py:94\u001B[0m, in \u001B[0;36mInitialize.__init__\u001B[0;34m(self, params, num_qubits)\u001B[0m\n\u001B[1;32m 92\u001B[0m \u001B[38;5;66;03m# Check if probabilities (amplitudes squared) sum to 1\u001B[39;00m\n\u001B[1;32m 93\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m math\u001B[38;5;241m.\u001B[39misclose(\u001B[38;5;28msum\u001B[39m(np\u001B[38;5;241m.\u001B[39mabsolute(params) \u001B[38;5;241m*\u001B[39m\u001B[38;5;241m*\u001B[39m \u001B[38;5;241m2\u001B[39m), \u001B[38;5;241m1.0\u001B[39m, abs_tol\u001B[38;5;241m=\u001B[39m_EPS):\n\u001B[0;32m---> 94\u001B[0m \u001B[38;5;28;01mraise\u001B[39;00m QiskitError(\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mSum of amplitudes-squared does not equal one.\u001B[39m\u001B[38;5;124m\"\u001B[39m)\n\u001B[1;32m 96\u001B[0m num_qubits \u001B[38;5;241m=\u001B[39m \u001B[38;5;28mint\u001B[39m(num_qubits)\n\u001B[1;32m 98\u001B[0m \u001B[38;5;28msuper\u001B[39m()\u001B[38;5;241m.\u001B[39m\u001B[38;5;21m__init__\u001B[39m(\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124minitialize\u001B[39m\u001B[38;5;124m\"\u001B[39m, num_qubits, \u001B[38;5;241m0\u001B[39m, params)\n", "\u001B[0;31mQiskitError\u001B[0m: 'Sum of amplitudes-squared does not equal one.'" ] } ], "source": [ "vector = [1,1]\n", "qc.initialize(vector, 0)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### In class exercise\n", "1. Create a state vector that will give a 1/3 probability of measuring $\\left|0\\right\\rangle$.\n", "2. Create a different state vector that will give the same measurement probabilities.\n", "3. Verify that the probability of measuring \\left|1\\right\\rangle for these two states is 2/3." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "##Fill me" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### Alternative measurement\n", "The measurement rule gives us the probability $p\\left(\\left|x\\right\\rangle\\right)$ that a state $\\left|\\psi\\right\\rangle$ is measured as $\\left|x\\right\\rangle$. Nowhere does it tell us that $\\left|x\\right\\rangle$ can only be either $\\left|0\\right\\rangle$ or $\\left|1\\right\\rangle$.\n", "\n", "The measurements we have considered so far are in fact only one of an infinite number of possible ways to measure a qubit. For any orthogonal pair of states, we can define a measurement that would cause a qubit to choose between the two.\n", "\n", "This possibility will be explored more in the next section. For now, just bear in mind that $\\left|x\\right\\rangle$ is not limited to being simply $\\left|0\\right\\rangle$ or $\\left|1\\right\\rangle$." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### Global Phase\n", "We know that measuring the state $\\left|1\\right\\rangle$ will give us the output $1$ with certainty. But we are also able to write down states such as\n", "\n", "$$\n", "\\begin{pmatrix} 0 \\\\ i \\end{pmatrix}=i\\left|1\\right\\rangle.\n", "$$\n", "\n", "To see how this behaves, we apply the measurement rule.\n", "\n", "$$\n", "\\left|\\left\\langle x \\right| \\left(i \\left|1\\right\\rangle\\right)\\right|^2=\\left|i\\left\\langle x\\middle|1\\right\\rangle\\right|^2=\\left|\\left\\langle x\\middle|1\\right\\rangle\\right|^2\n", "$$\n", "\n", "Here we find that the factor of $i$ disappears once we take the magnitude of the complex number. This effect is completely independent of the measured state $\\left|x\\right\\rangle$. It does not matter what measurement we are considering, the probabilities for the state $i\\left|1\\right\\rangle$ are identical to those for $\\left|1\\right\\rangle$. Since measurements are the only way we can extract any information from a qubit, this implies that these two states are equivalent in all ways that are physically relevant.\n", "\n", "More generally, we refer to any overall factor $\\gamma$ on a state for which $\\left|\\gamma\\right|=1$ as a 'global phase'. States that differ only by a global phase are physically indistinguishable.\n", "\n", "$$\n", "\\left|\\left\\langle x \\right| \\left(\\gamma \\left|\\alpha\\right\\rangle\\right)\\right|^2=\\left|\\gamma\\left\\langle x\\middle|\\alpha\\right\\rangle\\right|^2=\\left|\\left\\langle x\\middle|\\alpha\\right\\rangle\\right|^2\n", "$$\n", "\n", "Note that this is distinct from the phase difference between terms in a superposition, which is known as the 'relative phase'. This becomes relevant once we consider different types of measurement and multiple qubits.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "##### The Observer Effect\n", "\n", "We know that the amplitudes contain information about the probability of us finding the qubit in a specific state, but once we have measured the qubit, we know with certainty what the state of the qubit is. For example, if we measure a qubit in the state:\n", "\n", "$$\n", "\\left|q\\right\\rangle = \\alpha \\left|0\\right\\rangle + \\beta \\left|1\\right\\rangle\n", "$$\n", "\n", "And find it in the state $\\left|0\\right\\rangle$, if we measure again, there is a 100% chance of finding the qubit in the state $\\left|0\\right\\rangle$. This means the act of measuring changes the state of our qubits.\n", "\n", "$$\n", "\\left|q\\right\\rangle=\\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix} \\xrightarrow{\\text{Measure } \\left|0\\right\\rangle} \\left|q\\right\\rangle=\\left|0\\right\\rangle=\\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}\n", "$$\n", "\n", "We sometimes refer to this as collapsing the state of the qubit. It is a potent effect, and so one that must be used wisely. For example, were we to constantly measure each of our qubits to keep track of their value at each point in a computation, they would always simply be in a well-defined state of either $\\left|0\\right\\rangle$ or $\\left|1\\right\\rangle$. As such, they would be no different from classical bits and our computation could be easily replaced by a classical computation. To achieve truly quantum computation we must allow the qubits to explore more complex states. Measurements are therefore only used when we need to extract an output. This means that we often place all the measurements at the end of our quantum circuit.\n", "\n", "We can demonstrate this using Qiskit’s statevector simulator. Let's initialize a qubit in superposition:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1) # We are redefining qc\n", "initial_state = [0.+1.j/sqrt(2),1/sqrt(2)+0.j]\n", "qc.initialize(initial_state, 0)\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "This should initialize our qubit in the state:\n", "\n", "$$\n", "\\left|q_0\\right\\rangle = \\frac{i}{\\sqrt{2}} \\left|0\\right\\rangle + \\frac{1}{\\sqrt{2}} \\left|1\\right\\rangle\n", "$$\n", "\n", "We can verify this using the simulator:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Qubit State = Statevector([0. +0.70710678j, 0.70710678+0.j ],\n", " dims=(2,))\n" ] } ], "source": [ "qc.save_statevector()\n", "result = sim.run(assemble(qc)).result()\n", "state = result.get_statevector()\n", "print(\"Qubit State = \" + str(state))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "We can see here the qubit is initialized in the state [0.+0.70710678j 0.70710678+0.j], which is the state we expected.\n", "\n", "Let’s now create a circuit where we measure this qubit" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", 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" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1) # We are redefining qc\n", "initial_state = [0.+1.j/sqrt(2),1/sqrt(2)+0.j]\n", "qc.initialize(initial_state, 0)\n", "qc.measure_all()\n", "qc.save_statevector()\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "When we simulate this entire circuit, we can see that one of the amplitudes is always $0$:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State of Measured Qubit = Statevector([0.+0.j, 1.+0.j],\n", " dims=(2,))\n" ] } ], "source": [ "qobj = assemble(qc)\n", "state = sim.run(qobj).result().get_statevector()\n", "print(\"State of Measured Qubit = \" + str(state))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "You can re-run this cell a few times to reinitialize the qubit and measure it again. You will notice that either outcome is equally probable, but that the state of the qubit is never a superposition of $\\left|0\\right\\rangle$ and $\\left|1\\right\\rangle$. Somewhat interestingly, the global phase on the state $\\left|0\\right\\rangle$ survives, but since this is global phase, we can never measure it on a real quantum computer." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### A Note about Quantum Simulators\n", "\n", "We can see that writing down a qubit’s state requires keeping track of two complex numbers, but when using a real quantum computer we will only ever receive a yes-or-no (0 or 1) answer for each qubit. The output of a 10-qubit quantum computer will look like this:\n", "\n", "$$\n", "0110111110\n", "$$\n", "\n", "Just 10 bits, no superposition or complex amplitudes. When using a real quantum computer, we cannot see the states of our qubits mid-computation, as this would destroy them! This behaviour is not ideal for learning, so Qiskit provides different quantum simulators: By default, the `aer_simulator` mimics the execution of a real quantum computer, but will also allow you to peek at quantum states before measurement if we include certain instructions in our circuit. For example, here we have included the instruction `.save_statevector()`, which means we can use `.get_statevector()` on the result of the simulation." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## The Bloch Sphere\n", "\n", "We saw earlier in this chapter that the general state of a qubit $\\left|q\\right\\rangle$ is:\n", "\n", "$$\n", "\\left|q\\right\\rangle = \\alpha \\left|0\\right\\rangle + \\beta \\left|1\\right\\rangle \\\\\n", "\\alpha,\\beta \\in \\mathbb C\n", "$$\n", "\n", "(The second line tells us $\\alpha$ and $\\beta$ are complex numbers). We know that we cannot differentiate between some of these states. This means we can be more specific in our description of the qubit.\n", "\n", "Firstly, since we cannot measure global phase, we can only measure the difference in phase between the states $\\left|0\\right\\rangle$ and $\\left|1\\right\\rangle$. Instead of having $\\alpha$ and $\\beta$ be complex, we can confine them to the real numbers and add a term to tell us the relative phase between them:\n", "\n", "$$\n", "\\left|q\\right\\rangle = \\alpha \\left|0\\right\\rangle + e^{i\\phi}\\beta \\left|1\\right\\rangle \\\\\n", "\\alpha,\\beta,\\phi \\in \\mathbb R\n", "$$\n", "\n", "Finally, since the qubit state must be normalised, i.e.\n", "\n", "$$\n", "\\sqrt{\\alpha^2+\\beta^2}=1\n", "$$\n", "\n", "we can use the trigonometric identity:\n", "\n", "$$\n", "\\sqrt{\\sin^2 x+\\cos^2 x}=1\n", "$$\n", "\n", "to describe the real $\\alpha$ and $\\beta$ in terms of one variable, $\\theta$ :\n", "\n", "$$\n", "\\alpha=\\cos\\frac{\\theta}{2}\\qquad \\beta=\\sin\\frac{\\theta}{2}\n", "$$\n", "\n", "From this we can describe the state of any qubit using the two variables $\\phi$ and $\\theta$ :\n", "\n", "$$\n", "\\left|q\\right\\rangle = \\cos\\frac{\\theta}{2} \\left|0\\right\\rangle + e^{i\\phi}\\sin\\frac{\\theta}{2} \\left|1\\right\\rangle \\\\\n", "\\theta,\\phi \\in \\mathbb R\n", "$$\n", "\n", "If we interpret $\\phi$ and $\\theta$ as spherical co-ordinates ($r=1$, since the magnitude of the qubit state is 1), we can plot any single qubit state on the surface of a sphere, known as the _Bloch sphere_.\n", "\n", "Below we have plotted a qubit in the state $\\left|+\\right\\rangle$. In this case, $\\theta=\\pi/2$ and $\\phi=0$." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_bloch_vector(bloch=[1,pi/2,0],title='example',coord_type='spherical')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## In Class Exercise\n", "\n", "Use `plot_bloch_vector()` to plot a qubit in the states:\n", "\n", "1. $\\left|0\\right\\rangle$\n", "2. $\\left|1\\right\\rangle$\n", "3. $\\frac{1}{\\sqrt 2}\\left(\\left|0\\right\\rangle+\\left|1\\right\\rangle\\right)$\n", "4. $\\frac{1}{\\sqrt 2}\\left(\\left|0\\right\\rangle-i\\left|1\\right\\rangle\\right)$\n", "5. $\\frac{1}{\\sqrt 2} \\begin{pmatrix} i \\\\ 1 \\end{pmatrix} $" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "### Fill me" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Your first multi-qubit quantum circuit\n", "\n", "In a circuit, we typically need to do three jobs: First, encode the input, then do some actual computation, and finally extract an output. For your first quantum circuit, we'll focus on the last of these jobs. We start by creating a quantum circuit with 3 qubits and 3 outputs. Finally the method qc.draw() creates a drawing of the circuit for us. Jupyter Notebooks evaluate the last line of a code cell and display it below the cell. Since `qc.draw()` returns a drawing, that’s what we’re seeing under the code. There are no gates in our circuit yet, so we just see some horizontal lines. (_Return_ is another word for 'output'. In Python, we can use returned data as input to another function or process.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from qiskit import QuantumCircuit\n", "# Create quantum circuit with 3 qubits and 3 classical bits\n", "# (we'll explain why we need the classical bits later)\n", "qc = QuantumCircuit(3, 3)\n", "qc.draw(output='mpl') # returns a drawing of the circuit" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### What's a method?\n", "The `QuantumCircuit` class is a set of instructions for representing quantum circuits as bits, but when we want to change one of these circuits, we also need to know how to change the bits accordingly. In Python, objects come with ‘methods’, which are sets of instructions for doing something with that object. In the cell above, the `.draw()` method looks at the circuit we’ve created and produces a human-readable drawing of that circuit." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Next, we need a way to tell our quantum computer to measure our qubits and record the results. To do this, we add a \"measure\" operation to our quantum circuit. We can do this with the `QuantumCircuit`'s `.measure()` method." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# measure qubits 0, 1 & 2 to classical bits 0, 1 & 2 respectively\n", "qc.measure([0,1,2], [0,1,2])\n", "qc.draw(output='mpl')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Next, let's see what the results of running this circuit would be. To do this, we'll use a quantum simulator, which is a standard computer calculating what an ideal quantum computer would do. Because simulating a quantum computer is believed to be difficult for classical computers (the best algorithms we have grow exponentially with the number of qubits), these simulations are only possible for circuits with small numbers of qubits (up to ~30 qubits), or certain types of circuits for which we can use some tricks to speed up the simulation. Simulators are very useful tools for designing smaller quantum circuits.\n", "\n", "Let's import Qiskit’s simulator (called Aer), and make a new simulator object." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from qiskit.providers.aer import AerSimulator\n", "sim = AerSimulator() # make new simulator object" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "To do the simulation, we can use the simulators `.run()` method. This returns a \"job\", which contains information about the experiment, such as whether the experiment is running or completed, what backend we ran the experiment on, and importantly for us, what the results of the experiment are!\n", "\n", "To get the results from the job, we use the results method, and the most popular way to view the results is as a dictionary of \"counts\"." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "job = sim.run(qc) # run the experiment\n", "result = job.result() # get the results\n", "counts = result.get_counts() # interpret the results as a \"counts\" dictionary\n", "print(counts)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "The keys in counts dictionary are bit-strings, and the values are the number of times that bit-string was measured. Quantum computers can have randomness in their results, so it's common to repeat the circuit a few times. This circuit was repeated 1024 times, which is the default number of times to repeat a circuit in Qiskit. By convention, qubits always start in the state 0, and since we are doing nothing to them before measurement, the results are always `0`. This is not always the case. In actual situations, you will need a statistical method to analyse the output. Qiskit also provides a function `plot_histogram`, which allows you to view the outcomes." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from qiskit.visualization import plot_histogram\n", "plot_histogram(counts)\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### Basics of encoding an input\n", "\n", "Now let's look at how to encode a different binary string as an input. For this, we need what is known as a NOT gate. This is the most basic operation that you can do in a computer. It simply flips the bit value: 0 becomes 1 and 1 becomes 0. For qubits, we use a gate known as the _X-gate_ for this.\n", "\n", "Below, we’ll create a new circuit dedicated to the job of encoding:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Create quantum circuit with 3 qubits and 3 classical bits:\n", "qc = QuantumCircuit(3, 3)\n", "qc.x([0,1]) # Perform X-gates on qubits 0 & 1\n", "qc.measure([0,1,2], [0,1,2])\n", "qc.draw('mpl') # returns a drawing of the circuit" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "And let's simulate our circuit to see the results:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "job = sim.run(qc) # run the experiment\n", "result = job.result() # get the results\n", "counts=result.get_counts() # interpret the results as a \"counts\" dictionary\n", "print(counts)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "plot_histogram(counts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Single qubits are interesting, but individually they offer no computational advantage. We will now look at how we represent multiple qubits, and how these qubits can interact with each other. We have seen how we can represent the state of a qubit using a 2D-vector, now we will see how we can represent the state of multiple qubits." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Representing Multi-Qubit States\n", "\n", "We saw that a single bit has two possible states, and a qubit state has two complex amplitudes. Similarly, two bits have four possible states:\n", "\n", "`00` `01` `10` `11`\n", "\n", "And to describe the state of two qubits requires four complex amplitudes. We store these amplitudes in a 4D-vector like so:\n", "\n", "$$ |a\\rangle = a_{00}|00\\rangle + a_{01}|01\\rangle + a_{10}|10\\rangle + a_{11}|11\\rangle = \\begin{bmatrix} a_{00} \\\\ a_{01} \\\\ a_{10} \\\\ a_{11} \\end{bmatrix} $$\n", "\n", "The rules of measurement still work in the same way:\n", "\n", "$$ p(|00\\rangle) = |\\langle 00 | a \\rangle |^2 = |a_{00}|^2$$\n", "\n", "And the same implications hold, such as the normalisation condition:\n", "\n", "$$ |a_{00}|^2 + |a_{01}|^2 + |a_{10}|^2 + |a_{11}|^2 = 1$$\n", "\n", "If we have two separated qubits, we can describe their collective state using the kronecker product:\n", "\n", "$$ |a\\rangle = \\begin{bmatrix} a_0 \\\\ a_1 \\end{bmatrix}, \\quad |b\\rangle = \\begin{bmatrix} b_0 \\\\ b_1 \\end{bmatrix} $$\n", "\n", "$$ \n", "|ba\\rangle = |b\\rangle \\otimes |a\\rangle = \\begin{bmatrix} b_0 \\times \\begin{bmatrix} a_0 \\\\ a_1 \\end{bmatrix} \\\\ b_1 \\times \\begin{bmatrix} a_0 \\\\ a_1 \\end{bmatrix} \\end{bmatrix} = \\begin{bmatrix} b_0 a_0 \\\\ b_0 a_1 \\\\ b_1 a_0 \\\\ b_1 a_1 \\end{bmatrix}\n", "$$\n", "\n", "And following the same rules, we can use the kronecker product to describe the collective state of any number of qubits. Here is an example with three qubits:\n", "\n", "$$ \n", "|cba\\rangle = \\begin{bmatrix} c_0 b_0 a_0 \\\\ c_0 b_0 a_1 \\\\ c_0 b_1 a_0 \\\\ c_0 b_1 a_1 \\\\\n", " c_1 b_0 a_0 \\\\ c_1 b_0 a_1 \\\\ c_1 b_1 a_0 \\\\ c_1 b_1 a_1 \\\\\n", " \\end{bmatrix}\n", "$$\n", "\n", "If we have $n$ qubits, we will need to keep track of $2^n$ complex amplitudes. As we can see, these vectors grow exponentially with the number of qubits. This is the reason quantum computers with large numbers of qubits are so difficult to simulate. A modern laptop can easily simulate a general quantum state of around 20 qubits, but simulating 100 qubits is too difficult for the largest supercomputers.\n", "\n", "Let's look at an example circuit:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "from qiskit import QuantumCircuit, Aer, assemble\n", "import numpy as np\n", "from qiskit.visualization import plot_histogram, plot_bloch_multivector" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(3)\n", "# Apply H-gate to each qubit:\n", "for qubit in range(3):\n", " qc.h(qubit)\n", "# See the circuit:\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each qubit is in the state $|+\\rangle$, so we should see the vector:\n", "\n", "$$ \n", "|{+++}\\rangle = \\frac{1}{\\sqrt{8}}\\begin{bmatrix} 1 \\\\ 1 \\\\ 1 \\\\ 1 \\\\\n", " 1 \\\\ 1 \\\\ 1 \\\\ 1 \\\\\n", " \\end{bmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\n", "\\text{Statevector} = \n", "\\begin{bmatrix}\n", "\\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result\n", "svsim = Aer.get_backend('aer_simulator')\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "\n", "# In Jupyter Notebooks we can display this nicely using Latex.\n", "# If not using Jupyter Notebooks you may need to remove the \n", "# array_to_latex function and use print(final_state) instead.\n", "from qiskit.visualization import array_to_latex\n", "array_to_latex(final_state, prefix=\"\\\\text{Statevector} = \")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we have our expected result." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Single Qubit Gates on Multi-Qubit Statevectors\n", "\n", "We have seen that an X-gate is represented by the matrix:\n", "\n", "$$\n", "X = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix}\n", "$$\n", "\n", "And that it acts on the state $|0\\rangle$ as so:\n", "\n", "$$\n", "X|0\\rangle = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix}\\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} = \\begin{bmatrix} 0 \\\\ 1\\end{bmatrix}\n", "$$\n", "\n", "but it may not be clear how an X-gate would act on a qubit in a multi-qubit vector. Fortunately, the rule is quite simple; just as we used the kronecker product to calculate multi-qubit statevectors, we use the tensor product to calculate matrices that act on these statevectors. For example, in the circuit below:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "we can represent the simultaneous operations (H & X) using their kronecker product:\n", "\n", "$$\n", "X|q_1\\rangle \\otimes H|q_0\\rangle = (X\\otimes H)|q_1 q_0\\rangle\n", "$$\n", "\n", "The operation looks like this:\n", "\n", "$$\n", "X\\otimes H = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix} \\otimes \\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", "$$\n", "\n", "$$\n", "= \\frac{1}{\\sqrt{2}}\n", "\\begin{bmatrix} 0 \\times \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", " & 1 \\times \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", " \\\\ \n", " 1 \\times \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", " & 0 \\times \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", "\\end{bmatrix} \n", "$$\n", "\n", "$$\n", "= \\frac{1}{\\sqrt{2}}\n", "\\begin{bmatrix} 0 & 0 & 1 & 1 \\\\\n", " 0 & 0 & 1 & -1 \\\\\n", " 1 & 1 & 0 & 0 \\\\\n", " 1 & -1 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "Which we can then apply to our 4D statevector $|q_1 q_0\\rangle$. This can become quite messy, you will often see the clearer notation:\n", "\n", "$$\n", "X\\otimes H = \n", "\\begin{bmatrix} 0 & H \\\\\n", " H & 0\\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "Instead of calculating this by hand, we can use Qiskit’s `aer_simulator` to calculate this for us. The Aer simulator multiplies all the gates in our circuit together to compile a single unitary matrix that performs the whole quantum circuit:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "usim = Aer.get_backend('aer_simulator')\n", "qc.save_unitary()\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and view the results:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\n", "\\text{Circuit = }\n", "\n", "\\begin{bmatrix}\n", "0 & 0 & \\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}} \\\\\n", " 0 & 0 & \\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} \\\\\n", " \\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}} & 0 & 0 \\\\\n", " \\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} & 0 & 0 \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# In Jupyter Notebooks we can display this nicely using Latex.\n", "# If not using Jupyter Notebooks you may need to remove the \n", "# array_to_latex function and use print(unitary) instead.\n", "from qiskit.visualization import array_to_latex\n", "array_to_latex(unitary, prefix=\"\\\\text{Circuit = }\\n\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to apply a gate to only one qubit at a time (such as in the circuit below), we describe this using kronecker product with the identity matrix, e.g.:\n", "\n", "$$ X \\otimes I $$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.x(1)\n", "qc.draw('mpl')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\n", "\\text{Circuit = } \n", "\\begin{bmatrix}\n", "0 & 0 & 1 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 1 & 0 & 0 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Simulate the unitary\n", "usim = Aer.get_backend('aer_simulator')\n", "qc.save_unitary()\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()\n", "# Display the results:\n", "array_to_latex(unitary, prefix=\"\\\\text{Circuit = } \")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see Qiskit has performed the kronecker product:\n", "$$\n", "X \\otimes I =\n", "\\begin{bmatrix} 0 & I \\\\\n", " I & 0\\\\\n", "\\end{bmatrix} = \n", "\\begin{bmatrix} 0 & 0 & 1 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 1 & 0 & 0 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### Send it after class 1\n", "\n", "Calculate the single qubit unitary ($U$) created by the sequence of gates: $U = XZH$. Use Qiskit's Aer simulator to check your results.\n", "\n", "**Note:** Different books, softwares and websites order their qubits differently. This means the kronecker product of the same circuit can look very different. Try to bear this in mind when consulting other sources.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multi-Qubit Gates\n", "\n", "Now we know how to represent the state of multiple qubits, we are now ready to learn how qubits interact with each other. An important two-qubit gate is the CNOT-gate.\n", "\n", "#### The CNOT-Gate\n", "\n", "CNOT gate is a conditional gate that performs an X-gate on the second qubit (target), if the state of the first qubit (control) is $|1\\rangle$. The gate is drawn on a circuit like this, with `q0` as the control and `q1` as the target:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "# Apply CNOT\n", "qc.cx(0,1)\n", "# See the circuit:\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When our qubits are not in superposition of $|0\\rangle$ or $|1\\rangle$ (behaving as classical bits), this gate is very simple and intuitive to understand. We can use the classical truth table:\n", "\n", "| Input (t,c) | Output (t,c) |\n", "|:-----------:|:------------:|\n", "| 00 | 00 |\n", "| 01 | 11 |\n", "| 10 | 10 |\n", "| 11 | 01 |\n", "\n", "And acting on our 4D-statevector, it has one of the two matrices:\n", "\n", "$$\n", "\\text{CNOT} = \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 0 & 0 & 1 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", " \\end{bmatrix}, \\quad\n", "\\text{CNOT} = \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 0 & 0 & 1 & 0 \\\\\n", " \\end{bmatrix}\n", "$$\n", "\n", "depending on which qubit is the control and which is the target. Different books, simulators and papers order their qubits differently. In our case, the left matrix corresponds to the CNOT in the circuit above. This matrix swaps the amplitudes of $|01\\rangle$ and $|11\\rangle$ in our statevector:\n", "\n", "$$ \n", "|a\\rangle = \\begin{bmatrix} a_{00} \\\\ a_{01} \\\\ a_{10} \\\\ a_{11} \\end{bmatrix}, \\quad \\text{CNOT}|a\\rangle = \\begin{bmatrix} a_{00} \\\\ a_{11} \\\\ a_{10} \\\\ a_{01} \\end{bmatrix} \\begin{matrix} \\\\ \\leftarrow \\\\ \\\\ \\leftarrow \\end{matrix}\n", "$$\n", "\n", "We have seen how this acts on classical states, but let’s now see how it acts on a qubit in superposition. We will put one qubit in the state $|+\\rangle$:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "# Apply H-gate to the first:\n", "qc.h(0)\n", "qc.draw('mpl')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\n", "\\text{Statevector = }\n", "\\begin{bmatrix}\n", "\\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}} & 0 & 0 \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result:\n", "svsim = Aer.get_backend('aer_simulator')\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "# Print the statevector neatly:\n", "array_to_latex(final_state, prefix=\"\\\\text{Statevector = }\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, this produces the state $|0\\rangle \\otimes |{+}\\rangle = |0{+}\\rangle$:\n", "\n", "$$\n", "|0{+}\\rangle = \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |01\\rangle)\n", "$$\n", "\n", "And let’s see what happens when we apply the CNOT gate:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "# Apply H-gate to the first:\n", "qc.h(0)\n", "# Apply a CNOT:\n", "qc.cx(0,1)\n", "qc.draw('mpl')" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\n", "\\text{Statevector = }\n", "\\begin{bmatrix}\n", "\\tfrac{1}{\\sqrt{2}} & 0 & 0 & \\tfrac{1}{\\sqrt{2}} \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's get the result:\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "result = svsim.run(qobj).result()\n", "# Print the statevector neatly:\n", "final_state = result.get_statevector()\n", "array_to_latex(final_state, prefix=\"\\\\text{Statevector = }\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see we have the state:\n", "\n", "$$\n", "\\text{CNOT}|0{+}\\rangle = \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)\n", "$$ \n", "\n", "This state is very interesting to us, because it is _entangled._ This leads us neatly on to the next section." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Entangled States\n", "\n", "We saw in the previous section we could create the state:\n", "\n", "$$\n", "\\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)\n", "$$ \n", "\n", "This is known as a _Bell_ state. We can see that this state has 50% probability of being measured in the state $|00\\rangle$, and 50% chance of being measured in the state $|11\\rangle$. Most interestingly, it has a **0%** chance of being measured in the states $|01\\rangle$ or $|10\\rangle$. We can see this in Qiskit:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_histogram(result.get_counts())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This combined state cannot be written as two separate qubit states, which has interesting implications. Although our qubits are in superposition, measuring one will tell us the state of the other and collapse its superposition. For example, if we measured the top qubit and got the state $|1\\rangle$, the collective state of our qubits changes like so:\n", "\n", "$$\n", "\\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle) \\quad \\xrightarrow[]{\\text{measure}} \\quad |11\\rangle\n", "$$\n", "\n", "Even if we separated these qubits light-years away, measuring one qubit collapses the superposition and appears to have an immediate effect on the other. This is the [‘spooky action at a distance’](https://en.wikipedia.org/wiki/Quantum_nonlocality) that upset so many physicists in the early 20th century.\n", "\n", "It’s important to note that the measurement result is random, and the measurement statistics of one qubit are **not** affected by any operation on the other qubit. Because of this, there is **no way** to use shared quantum states to communicate. This is known as the no-communication theorem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Visualizing Entangled States\n", "\n", "We have seen that this state cannot be written as two separate qubit states, this also means we lose information when we try to plot our state on separate Bloch spheres:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_bloch_multivector(final_state)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given how we defined the Bloch sphere in the earlier chapters, it may not be clear how Qiskit even calculates the Bloch vectors with entangled qubits like this. In the single-qubit case, the position of the Bloch vector along an axis nicely corresponds to the expectation value of measuring in that basis. If we take this as _the_ rule of plotting Bloch vectors, we arrive at this conclusion above. This shows us there is _no_ single-qubit measurement basis for which a specific measurement is guaranteed. This contrasts with our single qubit states, in which we could always pick a single-qubit basis. Looking at the individual qubits in this way, we miss the important effect of correlation between the qubits. We cannot distinguish between different entangled states. For example, the two states:\n", "\n", "$$\\tfrac{1}{\\sqrt{2}}(|01\\rangle + |10\\rangle) \\quad \\text{and} \\quad \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)$$\n", "\n", "will both look the same on these separate Bloch spheres, despite being very different states with different measurement outcomes.\n", "\n", "How else could we visualize this statevector? This statevector is simply a collection of four amplitudes (complex numbers), and there are endless ways we can map this to an image. One such visualization is the _Q-sphere,_ here each amplitude is represented by a blob on the surface of a sphere. The size of the blob is proportional to the magnitude of the amplitude, and the colour is proportional to the phase of the amplitude. The amplitudes for $|00\\rangle$ and $|11\\rangle$ are equal, and all other amplitudes are 0:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qiskit.visualization import plot_state_qsphere\n", "plot_state_qsphere(final_state)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can clearly see the correlation between the qubits. The Q-sphere's shape has no significance, it is simply a nice way of arranging our blobs; the number of `0`s in the state is proportional to the states position on the Z-axis, so here we can see the amplitude of $|00\\rangle$ is at the top pole of the sphere, and the amplitude of $|11\\rangle$ is at the bottom pole of the sphere." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Send it after class 2\n", "1. Create a quantum circuit that produces the Bell state: $\\tfrac{1}{\\sqrt{2}}(|01\\rangle + |10\\rangle)$.\n", " Use the statevector simulator to verify your result.\n", " \n", "2. The circuit you created in question 1 transforms the state $|00\\rangle$ to $\\tfrac{1}{\\sqrt{2}}(|01\\rangle + |10\\rangle)$, calculate the unitary of this circuit using Qiskit's simulator. Verify this unitary does in fact perform the correct transformation.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exploring the CNOT-Gate\n", "\n", "We saw that we could entangle the two qubits by placing the control qubit in the state $|+\\rangle$:\n", "\n", "$$\n", "\\text{CNOT}|0{+}\\rangle = \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)\n", "$$\n", "\n", "But what happens if we put the second qubit in superposition?" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from qiskit import QuantumCircuit, Aer, assemble\n", "from math import pi\n", "import numpy as np\n", "from qiskit.visualization import plot_bloch_multivector, plot_histogram, array_to_latex" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.h(1)\n", "qc.cx(0,1)\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "In the circuit above, we have the CNOT acting on the state:\n", "\n", "$$ |{+}{+}\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle) $$\n", "\n", "Since the CNOT swaps the amplitudes of $|01\\rangle$ and $|11\\rangle$, we see no change:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\n", "\\text{Statevector} = \n", "\\begin{bmatrix}\n", "\\tfrac{1}{2} & \\tfrac{1}{2} & \\tfrac{1}{2} & \\tfrac{1}{2} \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.h(1)\n", "qc.cx(0,1)\n", "display(qc.draw('mpl')) # `display` is a command for Jupyter notebooks\n", "# similar to `print`, but for rich content\n", "\n", "# Let's see the result\n", "svsim = Aer.get_backend('aer_simulator')\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "display(array_to_latex(final_state, prefix=\"\\\\text{Statevector} = \"))\n", "plot_bloch_multivector(final_state)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Let’s put the target qubit in the state $|-\\rangle$, so it has a negative phase:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "qc.h(1)\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "This creates the state:\n", "\n", "$$ |{-}{+}\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle - |10\\rangle - |11\\rangle) $$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\n", "\\text{Statevector} = \n", "\\begin{bmatrix}\n", "\\tfrac{1}{2} & \\tfrac{1}{2} & -\\tfrac{1}{2} & -\\tfrac{1}{2} \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "qc.h(1)\n", "display(qc.draw('mpl'))\n", "# See the result\n", "qc1 = qc.copy()\n", "qc1.save_statevector()\n", "final_state = svsim.run(qc1).result().get_statevector()\n", "display(array_to_latex(final_state, prefix=\"\\\\text{Statevector} = \"))\n", "plot_bloch_multivector(final_state)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "If the CNOT acts on this state, we will swap the amplitudes of $|01\\rangle$ and $|11\\rangle$, resulting in the state:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{CNOT}|{-}{+}\\rangle & = \\tfrac{1}{2}(|00\\rangle - |01\\rangle - |10\\rangle + |11\\rangle) \\\\\n", " & = |{-}{-}\\rangle\n", "\\end{aligned}\n", "$$\n", "\n", "\n", "This is interesting, because it affects the state of the _control_ qubit while leaving the state of the _target_ qubit unchanged." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\n", "\\text{Statevector} = \n", "\\begin{bmatrix}\n", "\\tfrac{1}{2} & -\\tfrac{1}{2} & -\\tfrac{1}{2} & \\tfrac{1}{2} \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc.cx(0,1)\n", "display(qc.draw('mpl'))\n", "\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "display(array_to_latex(final_state, prefix=\"\\\\text{Statevector} = \"))\n", "plot_bloch_multivector(final_state)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "If you remember the H-gate transforms $|{+}\\rangle \\rightarrow |0\\rangle$ and $|{-}\\rangle \\rightarrow |1\\rangle$, we can see that wrapping a CNOT in H-gates has the equivalent behaviour of a CNOT acting in the opposite direction:\n", "\n", "![cnot_identity](images/identities_1.png)\n", "\n", "We can verify this using Qiskit's Aer simulator:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAANgAAAB7CAYAAAAWqE6tAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAJq0lEQVR4nO3df2zU9R3H8edd1x/MGqVepFIp0pZ289Z20K0STLw2UWzdVDYBIVsTK0kJZW7Mv9yk/kNtMtI/cC6ZZsskS7Rz7TrUWYluaw9IVVa7AXWbR4BSDqu2iJt1pUB7++Ok9oByd3Cffr/37euRfJPe5+4+3zef3IvP9z73vfu6QqFQCBExwm11ASJOpoCJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGPQlqwuwu/YeOHHKmn3nzIXvfsOafVvBiWOtgEVx4hQc/sjqKmYHJ461DhFFDFLARAxSwEQMUsBEDFLARAxSwEQMUsBEDFLARAxSwCTC2Dn4dBTOjVtdiTPYOmATExM0NzezePFiMjIyKC0txe/3U1RURF1dndXlXVJbYwX7djbG3G4Xhz+CX3XBYy9CQzv8pBV+vw9Ojlhd2fSSYaxtfarU+vXraW9vp6GhgbKyMrq7u1m3bh1DQ0M8+uijVpfnGD1H4fnu8N+hz9vOjsObh+Afx+AHd8L8uZaVl9RsG7CWlhZ27NhBV1cXPp8PgMrKSnp7e2lvb2fp0qUWV+gMpz6DF978IlhThYDRs/CbPfDTe8Htmunqkp9tDxGbmpqoqqqaDNd5BQUFpKamUlJSAkB/fz8+n4/CwkKKi4vZs2ePFeUmre5DMHGpdH0uFILhT+HQBzNXk5PYMmDBYJC+vj5Wr1590X0DAwN4vV7S09MB2LBhAw8++CCBQIBnn32WtWvXcubMmaj7cLlcMW1+f1fc9e976Ul+WXd9xPZ+YG/c/fj9XTHXeaXbb3e+SSh0mYQBoVCI2h89abyWZBnreNjyEDEYDAKQnZ0d0T46Oorf76e6uhqA4eFh9u7dy8svvwzA8uXLmT9/Pp2dndx9990zW/QU5fc/TvnKLRFtbY0V1hQThcudEsOLJoTbnTIj9cTL7mNtyxnM4/EAEAgEItq3bdvG4OAgZWVlQHg2mzdv3uRsBrBo0SKOHTsWdR+hUCimzeerSNw/LE4+X0XMdV7ptqqqPGodLpebX/zsMeO1JMtYx8OWM1heXh4lJSU0NTWRlZVFTk4ObW1tdHR0AEwGTK7e7YWw99D097uAa9KheMGMleQotpzB3G43ra2teL1eNm7cSG1tLR6Ph02bNpGSkjK5wJGbm8uHH37I2NjY5HOPHj3KwoULrSo96dx0PVQVh/++8EDRBbhc8P3bIcWWrxT7c4XinfMsVFNTw/79+zlw4MBk24oVK1i5ciX19fV0d3ezatUq+vv7SUtLS8g+n37Duq+x598Ij9w1M/t6+zC80QfDUz5Yzr8RvlUKeTfOTA1OHGtbHiJOp6enh2XLlkW0PfPMMzz00ENs376dtLQ0WlpaEhau2eS2fCjPgx+/EL695T7wXGttTU6QNAEbGRkhEAhQX18f0Z6Xl8fu3bstqspZpi4mKlyJkTQBy8zMZHxcZ6BKctFbVxGDFDARgxQwEYMUMBGDFDARgxQwEYMUMBGDkuZzMKvkWPhVeSv3bQUnjrUCFsVsuj6X1Zw41jpEFDFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIZ9NH0d4DJ05Zs++cuc48w3w6ThxrBSyKE6es+znn2caJY61DRBGDFDARg3SIKJz6DA4ch+DHX7T9/HWYPxdyb4CSBZCRal19yUwBm8UGP4FX98O7QbjwGlZHhsIbwB/+Bt9cBNWl4YvxSewUsFloIgR/eRd2HYTxieiPHzsXvgrm/uOw9jbw3my+RqfQe7BZZiIEL74dnrliCddUn56GX/vDF+uT2Chgs8yuA1cXkBDwu7fgX+8nrCRHU8Bmkf7h8GViL2f798Lb5YQIz4KjZxJWmmPZOmATExM0NzezePFiMjIyKC0txe/3U1RURF1dndXlJZ0/vnPxYsaV+uR/8Od3E9SZg9k6YOvXr2fr1q1s2LCB1157jTVr1rBu3TqOHDlCWVmZ1eVdUltjBft2NsbcPlOOn4Rjw4nt863DcM7Ci47adaynsu0qYktLCzt27KCrqwufzwdAZWUlvb29tLe3s3TpUosrTC69xxLf52dj8N6gVhUvx7YzWFNTE1VVVZPhOq+goIDU1FRKSkoAeOKJJygsLMTtdtPW1mZFqUlh4KShfj+O/pjZzJYBCwaD9PX1sXr16ovuGxgYwOv1kp4e/sSzqqqKXbt2cccdd8x0mUnlg/8Y6vcTM/06hS0PEYPBIADZ2dkR7aOjo/j9fqqrqyfbli9ffkX7cLlcMT3ugcc7ufmrFXH1ve+lJ3mnozmi7ezpEXK/dmdc/fj9XfxwRWVcz5lO/a9HSM24ZvJ2tJXC6e7f/Hzk7Z2vvMrDvm9fZXVhyTLWoVDsS0W2DJjH4wEgEAhwzz33TLZv27aNwcFB2y5wnFd+/+OUr9wS0dbWWGFNMZ87d/Z0RMASZfzM6YT3GQ87jvVUtgxYXl4eJSUlNDU1kZWVRU5ODm1tbXR0dAAkJGCx/i/09BvWfUfJ56ugrTExC+tPvQ5Hh764feFMdN75mWu6+y9U//AD/OmpxNTolLGeypbvwdxuN62trXi9XjZu3EhtbS0ej4dNmzaRkpIyucAhsVuQlVz9OoUtZzCAwsJCOjs7I9pqamq49dZbmTNnjkVVJa8lC2H3e4ntc04qFN2U2D6dxrYBu5Senh6WLVsW0dbQ0MBzzz3H0NAQBw8eZPPmzfj9fvLz8y2pcdWWrrjaZ8otHrh5LgQT+JsX5fmQZuEryK5jPZUtDxEvZWRkhEAgcNEHzFu3biUYDDI2NsbJkycJBoOWhcvOXC5YmcC1ocwMuMubuP6cKmlmsMzMTMbHLTwvxwEK5oHvK+D/9/SPiXVxY015OGRyeUkzg0li3LcEvp57dX18pyz8MwISXdLMYJIYKW6ouR1uyIS//jO+s+vnpMKqcii7xVR1zqOAzUIpbrh3CRQvgFf+Hv2zpxQ3LMkNP+e6L89MjU6hgM1it3jgkbvC5ykeGIDjH8NH/4VzE5CeCvOvD/+q1JKFcK3eb10RBUzIvg6yi62uwpm0yCFikAImYpAOEaPImTs7920FJ461KxTPl1tEJC46RBQxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzHo/7zXcj2rYMp7AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\n", "\\text{Circuit = }\n", "\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 0 & 0 & 1 & 0 \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.h(1)\n", "qc.cx(0,1)\n", "qc.h(0)\n", "qc.h(1)\n", "display(qc.draw('mpl'))\n", "\n", "qc.save_unitary()\n", "usim = Aer.get_backend('aer_simulator')\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()\n", "array_to_latex(unitary, prefix=\"\\\\text{Circuit = }\\n\")" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\n", "\\text{Circuit = }\n", "\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 0 & 0 & 1 & 0 \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.cx(1,0)\n", "display(qc.draw('mpl'))\n", "qc.save_unitary()\n", "\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()\n", "array_to_latex(unitary, prefix=\"\\\\text{Circuit = }\\n\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "This identity is an example of _phase kickback,_ which leads us neatly on to the next section...\n", "\n", "### Phase Kickback\n", "\n", "#### Explaining the CNOT Circuit Identity\n", "In the previous section we saw this identity:\n", "\n", "![cnot_identity](images/identities_1.png)\n", "\n", "This is an example of _kickback_ (or, _phase kickback_ ) which is very important and is used in almost every quantum algorithm. Kickback is where the eigenvalue added by a gate to a qubit is ‘kicked back’ into a different qubit via a controlled operation. For example, we saw that performing an X-gate on a $|{-}\\rangle$ qubit gives it the phase $-1$:\n", "\n", "$$\n", "X|{-}\\rangle = -|{-}\\rangle\n", "$$\n", "\n", "When our control qubit is in either $|0\\rangle$ or $|1\\rangle$, this phase affects the whole state, however it is a global phase and has no observable effects:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{CNOT}|{-}0\\rangle & = |{-}\\rangle \\otimes |0\\rangle \\\\\n", " & = |{-}0\\rangle \\\\\n", " \\quad & \\\\\n", "\\text{CNOT}|{-}1\\rangle & = X|{-}\\rangle \\otimes |1\\rangle \\\\\n", " & = -|{-}\\rangle \\otimes |1\\rangle \\\\\n", " & = -|{-}1\\rangle \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "The interesting effect is when our control qubit is in superposition. The component of the control qubit that lies in the direction of $|1\\rangle$ applies this phase factor to the *corresponding* target qubit. This applied phase factor in turn introduces a relative phase into the control qubit:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{CNOT}|{-}{+}\\rangle & = \\tfrac{1}{\\sqrt{2}}(\\text{CNOT}|{-}0\\rangle + \\text{CNOT}|{-}1\\rangle) \\\\\n", " & = \\tfrac{1}{\\sqrt{2}}(|{-}0\\rangle + X|{-}1\\rangle) \\\\\n", " & = \\tfrac{1}{\\sqrt{2}}(|{-}0\\rangle -|{-}1\\rangle) \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "This can then be written as the two separable qubit states:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{CNOT}|{-}{+}\\rangle & = |{-}\\rangle \\otimes \\tfrac{1}{\\sqrt{2}}(|{0}\\rangle - |1\\rangle )\\\\\n", " & = |{-}{-}\\rangle \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "Wrapping the CNOT in H-gates transforms the qubits from the computational basis to the $(|+\\rangle, |-\\rangle)$ basis, where we see this effect. This identity is very useful in hardware, since some hardwares only allow for CNOTs in one direction between two specific qubits. We can use this identity to overcome this problem and allow CNOTs in both directions." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### Kickback with the T-gate \n", "\n", "Let’s look at another controlled operation, the controlled-T gate:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.cp(pi/4, 0, 1)\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "The T-gate has the matrix:\n", "\n", "$$\n", "\\text{T} =\n", "\\begin{bmatrix}\n", "1 & 0 \\\\\n", "0 & e^{i\\pi/4}\\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "And the controlled-T gate has the matrix:\n", "\n", "$$\n", "\\text{Controlled-T} =\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & e^{i\\pi/4}\\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "We can verify this using Qiskit's Aer simulator:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\n", "\\text{Controlled-T} = \n", "\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", " 0 & 0 & 1 & 0 \\\\\n", " 0 & 0 & 0 & \\tfrac{1}{\\sqrt{2}}(1 + i) \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.cp(pi/4, 0, 1)\n", "display(qc.draw('mpl'))\n", "# See Results:\n", "qc.save_unitary()\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()\n", "array_to_latex(unitary, prefix=\"\\\\text{Controlled-T} = \\n\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "More generally, we can find the matrix of any controlled-U operation using the rule:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{U} & =\n", "\\begin{bmatrix}\n", "u_{00} & u_{01} \\\\\n", "u_{10} & u_{11}\\\\\n", "\\end{bmatrix} \\\\\n", "\\quad & \\\\\n", "\\text{Controlled-U} & =\n", "\\begin{bmatrix}\n", "I & 0 \\\\\n", "0 & U\\\\\n", "\\end{bmatrix}\n", " =\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & u_{00} & u_{01} \\\\\n", "0 & 0 & u_{10} & u_{11}\\\\\n", "\\end{bmatrix}\n", "\\end{aligned}\n", "$$\n", "\n", "Qiskit puts the most significant bit (MSB) on the left, and the least significant bit (LSB) on the right. This is the standard ordering of binary bitstrings. We order the qubits in the same way (qubit representing the MSB has index 0), which is why Qiskit uses a non-standard tensor product order. Hence, in Qiskit, the above matrix looks like the following:\n", "\n", "$$\n", "\\text{Controlled-U} =\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & u_{00} & 0 & u_{01} \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & u_{10} & 0 & u_{11}\\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "\n", "If we apply the T-gate to a qubit in the state $|1\\rangle$, we add a phase of $e^{i\\pi/4}$ to this qubit:\n", "\n", "$$\n", "T|1\\rangle = e^{i\\pi/4}|1\\rangle\n", "$$\n", "\n", "This is _global phase_ and is unobservable. But if we control this operation using another qubit in the $|{+}\\rangle$ state, the phase is no longer global but relative, which changes the _relative phase_ in our control qubit:\n", "\n", "$$\n", "\\begin{aligned}\n", "|1{+}\\rangle & = |1\\rangle \\otimes \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) \\\\\n", "& = \\tfrac{1}{\\sqrt{2}}(|10\\rangle + |11\\rangle) \\\\\n", "& \\\\\n", "\\text{Controlled-T}|1{+}\\rangle & = \\tfrac{1}{\\sqrt{2}}(|10\\rangle + e^{i\\pi/4}|11\\rangle) \\\\\n", "& \\\\\n", "& = |1\\rangle \\otimes \\tfrac{1}{\\sqrt{2}}(|0\\rangle + e^{i\\pi/4}|1\\rangle)\n", "\\end{aligned}\n", "$$\n", "\n", "This has the effect of rotating our control qubit around the Z-axis of the Bloch sphere, while leaving the target qubit unchanged. Let's see this in Qiskit:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "display(qc.draw('mpl'))\n", "# See Results:\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "plot_bloch_multivector(final_state)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "# Add Controlled-T\n", "qc.cp(pi/4, 0, 1)\n", "display(qc.draw('mpl'))\n", "# See Results:\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "plot_bloch_multivector(final_state)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "we can see the leftmost qubit has been rotated by $\\pi/4$ around the Z-axis of the Bloch sphere as expected. After exploring this behaviour, it may become clear why Qiskit draws the controlled-Z rotation gates in this symmetrical fashion (two controls instead of a control and a target). There is no clear control or target qubit for all cases.\n", "\n", "![](images/pkb_z_equiv.png)\n", "\n", "#### Send it after class :\n", "\n", "-What would be the resulting state of the control qubit (q0) if the target qubit (q1) was in the state $|0\\rangle$? (as shown in the circuit below)? Use Qiskit to check your answer.\n", "\n", "\n", "\n", "![](images/pkb_ex1.png)\n", "\n", "-What would happen to the control qubit (q0) if the target qubit (q1) was in the state $|1\\rangle$, and the circuit used a controlled-Sdg gate instead of the controlled-T (as shown in the circuit below)?\n", "\n", "\n", "\n", "![](images/pkb_ex2.png)\n", "\n", "-What would happen to the control qubit (q0) if it was in the state $|1\\rangle$ instead of the state $|{+}\\rangle$ before application of the controlled-T (as shown in the circuit below)?\n", "\n", "\n", "\n", "![](images/pkb_ex3.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Single Qubit Gates\n", "In the previous section we looked at all the possible states a qubit could be in. We saw that qubits could be represented by 2D vectors, and that their states are limited to the form:\n", "\n", "$$ |q\\rangle = \\cos{\\tfrac{\\theta}{2}}|0\\rangle + e^{i\\phi}\\sin{\\tfrac{\\theta}{2}}|1\\rangle $$\n", "\n", "Where $\\theta$ and $\\phi$ are real numbers. In this section we will cover _gates,_ the operations that change a qubit between these states. Due to the number of gates and the similarities between them, this chapter is at risk of becoming a list. To counter this, we have included a few digressions to introduce important ideas at appropriate places throughout the chapter. \n", "\n", "In _The Atoms of Computation_ we came across some gates and used them to perform a classical computation. An important feature of quantum circuits is that, between initialising the qubits and measuring them, the operations (gates) are *_always_* reversible! These reversible gates can be represented as matrices, and as rotations around the Bloch sphere." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "from qiskit import QuantumCircuit, assemble, Aer\n", "from math import pi, sqrt\n", "from qiskit.visualization import plot_bloch_multivector, plot_histogram\n", "sim = Aer.get_backend('aer_simulator')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1. The Pauli Gates\n", "You should be familiar with the Pauli matrices from the linear algebra section. If any of the maths here is new to you, you should use the linear algebra section to bring yourself up to speed. We will see here that the Pauli matrices can represent some very commonly used quantum gates.\n", "\n", "#### 1.1 The X-Gate\n", "The X-gate is represented by the Pauli-X matrix:\n", "\n", "$$ X = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix} = |0\\rangle\\langle1| + |1\\rangle\\langle0| $$\n", "\n", "To see the effect a gate has on a qubit, we simply multiply the qubit’s statevector by the gate. We can see that the X-gate switches the amplitudes of the states $|0\\rangle$ and $|1\\rangle$:\n", "\n", "$$ X|0\\rangle = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix}\\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} = |1\\rangle$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In Qiskit, we can create a short circuit to verify this:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's do an X-gate on a |0> qubit\n", "qc = QuantumCircuit(1)\n", "qc.x(0)\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see the result of the above circuit. **Note:** Here we use `plot_bloch_multivector()` which takes a qubit's statevector instead of the Bloch vector." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "state = sim.run(qobj).result().get_statevector()\n", "plot_bloch_multivector(state)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can indeed see the state of the qubit is $|1\\rangle$ as expected. We can think of this as a rotation by $\\pi$ radians around the *x-axis* of the Bloch sphere. The X-gate is also often called a NOT-gate, referring to its classical analogue.\n", "\n", "#### 1.2 The Y & Z-gates\n", "Similarly to the X-gate, the Y & Z Pauli matrices also act as the Y & Z-gates in our quantum circuits:\n", "\n", "\n", "$$ Y = \\begin{bmatrix} 0 & -i \\\\ i & 0 \\end{bmatrix} \\quad\\quad\\quad\\quad Z = \\begin{bmatrix} 1 & 0 \\\\ 0 & -1 \\end{bmatrix} $$\n", "\n", "$$ Y = -i|0\\rangle\\langle1| + i|1\\rangle\\langle0| \\quad\\quad Z = |0\\rangle\\langle0| - |1\\rangle\\langle1| $$\n", "\n", "And, unsurprisingly, they also respectively perform rotations by $\\pi$ around the y and z-axis of the Bloch sphere.\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "In Qiskit, we can apply the Y and Z-gates to our circuit using:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc.y(0) # Do Y-gate on qubit 0\n", "qc.z(0) # Do Z-gate on qubit 0\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. Digression: The X, Y & Z-Bases" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Reminder: Eigenvectors of Matrices\n", "We have seen that multiplying a vector by a matrix results in a vector:\n", " \n", "$$\n", " M|v\\rangle = |v'\\rangle \\leftarrow \\text{new vector}\n", " $$\n", "If we chose the right vectors and matrices, we can find a case in which this matrix multiplication is the same as doing a multiplication by a scalar:\n", " \n", "$$\n", " M|v\\rangle = \\lambda|v\\rangle\n", " $$\n", "(Above, $M$ is a matrix, and $\\lambda$ is a scalar). For a matrix $M$, any vector that has this property is called an eigenvector of $M$. For example, the eigenvectors of the Z-matrix are the states $|0\\rangle$ and $|1\\rangle$:\n", "\n", "$$\n", " \\begin{aligned}\n", " Z|0\\rangle & = |0\\rangle \\\\\n", " Z|1\\rangle & = -|1\\rangle\n", " \\end{aligned}\n", " $$\n", "Since we use vectors to describe the state of our qubits, we often call these vectors eigenstates in this context. Eigenvectors are very important in quantum computing, and it is important you have a solid grasp of them.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may also notice that the Z-gate appears to have no effect on our qubit when it is in either of these two states. This is because the states $|0\\rangle$ and $|1\\rangle$ are the two _eigenstates_ of the Z-gate. In fact, the _computational basis_ (the basis formed by the states $|0\\rangle$ and $|1\\rangle$) is often called the Z-basis. This is not the only basis we can use, a popular basis is the X-basis, formed by the eigenstates of the X-gate. We call these two vectors $|+\\rangle$ and $|-\\rangle$:\n", "\n", "$$ |+\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) = \\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix}$$\n", "\n", "$$ |-\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle) = \\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 \\\\ -1 \\end{bmatrix} $$\n", "\n", "Another less commonly used basis is that formed by the eigenstates of the Y-gate. These are called:\n", "\n", "$$ |\\circlearrowleft\\rangle, \\quad |\\circlearrowright\\rangle$$\n", "\n", "We leave it as an exercise to calculate these. There are in fact an infinite number of bases; to form one, we simply need two orthogonal vectors. The eigenvectors of both Hermitian and unitary matrices form a basis for the vector space. Due to this property, we can be sure that the eigenstates of the X-gate and the Y-gate indeed form a basis for 1-qubit states (read more about this in the [linear algebra page](https://qiskit.org/textbook/ch-appendix/linear_algebra.html#Matrices-and-Matrix-Operations) in the appendix)\n", "\n", "#### Send it after class\n", "1. Verify that $|+\\rangle$ and $|-\\rangle$ are in fact eigenstates of the X-gate.\n", "2. What eigenvalues do they have? \n", "3. Find the eigenstates of the Y-gate, and their co-ordinates on the Bloch sphere.\n", "\n", "Using only the Pauli-gates it is impossible to move our initialized qubit to any state other than $|0\\rangle$ or $|1\\rangle$, i.e. we cannot achieve superposition. This means we can see no behaviour different to that of a classical bit. To create more interesting states we will need more gates!\n", "\n", "### 3. The Hadamard Gate\n", "\n", "The Hadamard gate (H-gate) is a fundamental quantum gate. It allows us to move away from the poles of the Bloch sphere and create a superposition of $|0\\rangle$ and $|1\\rangle$. It has the matrix:\n", "\n", "$$ H = \\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix} $$\n", "\n", "We can see that this performs the transformations below:\n", "\n", "$$ H|0\\rangle = |+\\rangle $$\n", "\n", "$$ H|1\\rangle = |-\\rangle $$\n", "\n", "This can be thought of as a rotation around the Bloch vector `[1,0,1]` (the line between the x & z-axis), or as transforming the state of the qubit between the X and Z bases.\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Create the X-measurement function:\n", "def x_measurement(qc, qubit, cbit):\n", " \"\"\"Measure 'qubit' in the X-basis, and store the result in 'cbit'\"\"\"\n", " qc.h(qubit)\n", " qc.measure(qubit, cbit)\n", " return qc\n", "\n", "initial_state = [1/sqrt(2), -1/sqrt(2)]\n", "# Initialize our qubit and measure it\n", "qc = QuantumCircuit(1,1)\n", "qc.initialize(initial_state, 0)\n", "x_measurement(qc, 0, 0) # measure qubit 0 to classical bit 0\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the quick exercises above, we saw you could create an X-gate by sandwiching our Z-gate between two H-gates:\n", "\n", "$$ X = HZH $$\n", "\n", "Starting in the Z-basis, the H-gate switches our qubit to the X-basis, the Z-gate performs a NOT in the X-basis, and the final H-gate returns our qubit to the Z-basis. We can verify this always behaves like an X-gate by multiplying the matrices:\n", "\n", "$$\n", "HZH =\n", "\\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", "\\begin{bmatrix} 1 & 0 \\\\ 0 & -1 \\end{bmatrix}\n", "\\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", "=\n", "\\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix}\n", "=X\n", "$$\n", "\n", "Following the same logic, we have created an X-measurement by transforming from the X-basis to the Z-basis before our measurement. Since the process of measuring can have different effects depending on the system (e.g. some systems always return the qubit to $|0\\rangle$ after measurement, whereas others may leave it as the measured state), the state of the qubit post-measurement is undefined and we must reset it if we want to use it again.\n", "\n", "There is another way to see why the Hadamard gate indeed takes us from the Z-basis to the X-basis. Suppose the qubit we want to measure in the X-basis is in the (normalized) state $a |0\\rangle + b |1\\rangle$. To measure it in X-basis, we first express the state as a linear combination of $|+\\rangle$ and $|-\\rangle$. Using the relations $|0\\rangle = \\frac{|+\\rangle + |-\\rangle}{\\sqrt{2}}$ and $|1\\rangle = \\frac{|+\\rangle - |-\\rangle}{\\sqrt{2}}$, the state becomes $\\frac{a + b}{\\sqrt{2}}|+\\rangle + \\frac{a - b}{\\sqrt{2}}|-\\rangle$. Observe that the probability amplitudes in X-basis can be obtained by applying a Hadamard matrix on the state vector expressed in Z-basis.\n", "\n", "Let’s now see the results:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qobj = assemble(qc) # Assemble circuit into a Qobj that can be run\n", "counts = sim.run(qobj).result().get_counts() # Do the simulation, returning the state vector\n", "plot_histogram(counts) # Display the output on measurement of state vector" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We initialized our qubit in the state $|-\\rangle$, but we can see that, after the measurement, we have collapsed our qubit to the state $|1\\rangle$. If you run the cell again, you will see the same result, since along the X-basis, the state $|-\\rangle$ is a basis state and measuring it along X will always yield the same result.\n", "\n", "\n", "\n", "\n", "Measuring in different bases allows us to see Heisenberg’s famous uncertainty principle in action. Having certainty of measuring a state in the Z-basis removes all certainty of measuring a specific state in the X-basis, and vice versa. A common misconception is that the uncertainty is due to the limits in our equipment, but here we can see the uncertainty is actually part of the nature of the qubit. \n", "\n", "For example, if we put our qubit in the state $|0\\rangle$, our measurement in the Z-basis is certain to be $|0\\rangle$, but our measurement in the X-basis is completely random! Similarly, if we put our qubit in the state $|-\\rangle$, our measurement in the X-basis is certain to be $|-\\rangle$, but now any measurement in the Z-basis will be completely random.\n", "\n", "More generally: _Whatever state our quantum system is in, there is always a measurement that has a deterministic outcome._ \n", "\n", "The introduction of the H-gate has allowed us to explore some interesting phenomena, but we are still very limited in our quantum operations. Let us now introduce a new type of gate:\n", "\n", "### 5. The P-gate\n", "\n", "The P-gate (phase gate) is _parametrised,_ that is, it needs a number ($\\phi$) to tell it exactly what to do. The P-gate performs a rotation of $\\phi$ around the Z-axis direction. It has the matrix form:\n", "\n", "$$\n", "P(\\phi) = \\begin{bmatrix} 1 & 0 \\\\ 0 & e^{i\\phi} \\end{bmatrix}\n", "$$\n", "\n", "Where $\\phi$ is a real number.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In Qiskit, we specify a P-gate using `p(phi, qubit)`:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.p(pi/4, 0)\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may notice that the Z-gate is a special case of the P-gate, with $\\phi = \\pi$. In fact there are three more commonly referenced gates we will mention in this chapter, all of which are special cases of the P-gate:\n", "\n", "### 6. The I, S and T-gates\n", "\n", "#### 6.1 The I-gate\n", "\n", "First comes the I-gate (aka ‘Id-gate’ or ‘Identity gate’). This is simply a gate that does nothing. Its matrix is the identity matrix:\n", "\n", "$$\n", "I = \\begin{bmatrix} 1 & 0 \\\\ 0 & 1\\end{bmatrix}\n", "$$\n", "\n", "Applying the identity gate anywhere in your circuit should have no effect on the qubit state, so it’s interesting this is even considered a gate. There are two main reasons behind this, one is that it is often used in calculations, for example: proving the X-gate is its own inverse:\n", "\n", "$$ I = XX $$\n", "\n", "The second, is that it is often useful when considering real hardware to specify a ‘do-nothing’ or ‘none’ operation.\n", "\n", "\n", "#### 6.2 The S-gates\n", "\n", "The next gate to mention is the S-gate (sometimes known as the $\\sqrt{Z}$-gate), this is a P-gate with $\\phi = \\pi/2$. It does a quarter-turn around the Bloch sphere. It is important to note that unlike every gate introduced in this chapter so far, the S-gate is **not** its own inverse! As a result, you will often see the S†-gate, (also “S-dagger”, “Sdg” or $\\sqrt{Z}^\\dagger$-gate). The S†-gate is clearly an P-gate with $\\phi = -\\pi/2$:\n", "\n", "$$ S = \\begin{bmatrix} 1 & 0 \\\\ 0 & e^{\\frac{i\\pi}{2}} \\end{bmatrix}, \\quad S^\\dagger = \\begin{bmatrix} 1 & 0 \\\\ 0 & e^{-\\frac{i\\pi}{2}} \\end{bmatrix}$$\n", "\n", "The name \"$\\sqrt{Z}$-gate\" is due to the fact that two successively applied S-gates has the same effect as one Z-gate:\n", "\n", "$$ SS|q\\rangle = Z|q\\rangle $$\n", "\n", "This notation is common throughout quantum computing.\n", "\n", "To add an S-gate in Qiskit:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKAAAABOCAYAAACngR3fAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAEeklEQVR4nO3dfUjcdQDH8c/deTvPhy3zxgy3KPFheOwMb5HQwymjYQVBC2kG1sQyD1mE//SEELXuDydUK4Jtzcw/smFdDTYagXjXSmqZjZCFRnswTfIyN3M5muf1x9A0l/x0s8/v5ucF98+J3gd9f++np6AlFovFIEJiZQ+QlU0BCpUCFCoFKFQKUKgUoFApQKFSgEKlAIVKAQqVAhQqBShUClCoFKBQKUChUoBCpQCFSgEKlQIUKgUoVApQqBSgUClAoVKAQqUAhUoBCpUCFKoE9gCWYBcwOMp57Mw0YNvmpb0va/fVbF7Iig1wcBT4aZi9YvHidfd/0SVYqBSgUClAoVKAQqUAhUoBCpUCXMHGImfw2d4d1A0KUKhMF+DU1BQaGxuRk5ODxMREFBQUIBwOIy8vD9XV1ex5OD98Ckf2lGF/bQberkrBgac34PBrDyE6+Rd72qKE3tuJT9/ajrPfH8WHu4rx6+lvKTtM95uQqqoqBINB1NfXw+v1orOzE+Xl5YhEIqirq2PPw6Hd9+PmTVvx2O5erHKuxvjvgzh94jDM9N8uzg+fwhcfPItfeo/h0sVxOJLTsO7Wzbhv50HYElYBAIoffxNjkTP4KvgStj7VTNtqqgBbW1vR3NyMUCgEn88HACgpKUF3dzeCwSAKCwup+yb+GMHoUC8eeCYIR9IaAEBq+np4ttRQd/1bPBySaaa6BAcCAZSWls7ENy07Oxt2ux0ej4e07DJnajrS17vR/s4T+OFYC0YGT5ruizp9SDZtqYEjaQ0sFsvMIUmwO9jz5jFNgAMDA+jp6UFZWdm8t/X398PtdsPh4H8CH34xhMyNxfju6Ot4/4XbsL92Hb7++BXThBgPh2Q2UwUIABkZGXPun5iYQDgcNnz5tVgshm7hcGhJO52pLtz5SACPvtqNmn3ncNf2Bhz/5GWc/Pxdwx8jHA4Z3rmU3UYPic2eiLSbNi7LZqNME6DL5QIA9PX1zbm/oaEBQ0ND8Hq9jFkLsjuSkH/PDrg2eBA5e4I9Z4bRQ5J8QwZuf/A50srLTBNgVlYWPB4PAoEAWlpa0N7eDr/fj6amJgAwHGAsFjN08/mKF73x4oVRfHnwefz2cw+ik5cwFZ3Ej8c/wshADzLz7jb8cXy+YsM7r3b3tToki91slGkCtFqtaGtrg9vtht/vR2VlJVwuF2pra2Gz2eg/gACAzbYKf44N48gb27C35kbs86/FN4d2wVexBzl3zP/eleFaHZL/i6lehsnNzUVHR8ec+yoqKpCfnw+n00la9Q97YjLuffIAe8aCZh+SC+eGYLUmYPXaW0x1SGYzVYBX0tXVhaKiIvaMuBEPh2Q201yCr2R8fBx9fX30F6Bl+Zj6GTAlJQXRaJQ9Q5aRqZ8B5fqnAIVKAQqVAhQqBShUClCoFKBQmfp1wOWUmRafj83avVyPa4mZ+a8V5bqnS7BQKUChUoBCpQCFSgEKlQIUKgUoVApQqBSgUClAoVKAQqUAhUoBCpUCFCoFKFQKUKgUoFApQKH6GzwvyzL75/7eAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.s(0) # Apply S-gate to qubit 0\n", "qc.sdg(0) # Apply Sdg-gate to qubit 0\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.3 The T-gate\n", "The T-gate is a very commonly used gate, it is an P-gate with $\\phi = \\pi/4$:\n", "\n", "$$ T = \\begin{bmatrix} 1 & 0 \\\\ 0 & e^{\\frac{i\\pi}{4}} \\end{bmatrix}, \\quad T^\\dagger = \\begin{bmatrix} 1 & 0 \\\\ 0 & e^{-\\frac{i\\pi}{4}} \\end{bmatrix}$$\n", "\n", "As with the S-gate, the T-gate is sometimes also known as the $\\sqrt[4]{Z}$-gate.\n", "\n", "In Qiskit:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKAAAABOCAYAAACngR3fAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAADUElEQVR4nO3dT0iacQDG8UfLucB2EAmhsUOEjgQPeen2VqcuwS5CHYJFoxFtl4IxGMEu8yCsQxtEsYPsUmDIYNBhh+V76TLp1CVPkUKtIAYJMZa5U7HoD+9q7vlpzweCeEN8hK/vmyLoqlQqFYiQuNkD5HZTgEKlAIVKAQqVAhQqBShUClCoFKBQKUChUoBCpQCFSgEKlQIUKgUoVApQqBSgUClAoVKAQqUAhUoBCpUCFCoFKFQKUKgUoFApQKFSgEKlAIWqkT2AZeMrcLDLue/mFiDce73bsnbfZPNVbm2AB7vAjyJ7xd+r1d2X0SVYqBSgUClAoVKAQqUAhUoBCpUCvKV29jeRXHzMnqEAhcu4N6KPj48xPT2Nubk5FAoFhMNhzMzMYHR0FJZlYX5+nrKr/5Xv9PdfRz8BAJ5G7+mxz29K/33Tdb3/9BwbhW/4vr+JydluPO1/i9D9GGWLcQGOjIwgk8lgamoKsVgMq6urGBwcxN7eHiYmJmi7/gzsbfoJyuUjvBhI0fZcxskT5dmjd9jZ38THL6/pj8GoABcWFpBKpZDNZmFZFgCgp6cHa2tryGQy6OzsJC80X608UU4Y9T9gIpFAX1/faXwn2tvb4fF4EI1GScukWowJsFgsYn19HfF4/Nzftra2EIlE4PV6L7il1DKjAgSAYDB45vjh4SFs23Z8+XW5XI5+bDv7rx+CY7addbyzWrvvNN7Fg5aHVdvslDEBBgIBAEA+nz9zPJlMYnt7G7EY51VavfLfC2Kg9yV7hjkvQtra2hCNRpFIJOD3+9Ha2oqlpSUsLy8DgOMAnX73Ym6R97k6y+pGZfZ63xHJ2n2TzVcx5gzodruRTqcRiUQwNjaG4eFhBAIBjI+Po6GhQS9A6pQxZ0AACIVCWFlZOXNsaGgIHR0daGpqIq06bzL+gT2hbhgV4EVyuRy6urrYM2pSLTxRjLkEX6RUKiGfz+sN6Dpm9BnQ5/OhXC6zZ0gVGX0GlPqnAIVKAQqVAhQqBShUClCoFKBQGf0+YDU1t9TmfbN2V+t+XRWnHx8RqQJdgoVKAQqVAhQqBShUClCoFKBQKUChUoBCpQCFSgEKlQIUKgUoVApQqBSgUClAoVKAQqUAhUoBCtVvTPvOKE9xXGsAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.t(0) # Apply T-gate to qubit 0\n", "qc.tdg(0) # Apply Tdg-gate to qubit 0\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 7. The U-gate\n", "\n", "As we saw earlier, the I, Z, S & T-gates were all special cases of the more general P-gate. In the same way, the U-gate is the most general of all single-qubit quantum gates. It is a parametrised gate of the form:\n", "\n", "$$\n", "U(\\theta, \\phi, \\lambda) = \\begin{bmatrix} \\cos(\\frac{\\theta}{2}) & -e^{i\\lambda}\\sin(\\frac{\\theta}{2}) \\\\\n", " e^{i\\phi}\\sin(\\frac{\\theta}{2}) & e^{i(\\phi+\\lambda)}\\cos(\\frac{\\theta}{2})\n", " \\end{bmatrix}\n", "$$\n", "\n", "Every gate in this chapter could be specified as $U(\\theta,\\phi,\\lambda)$, but it is unusual to see this in a circuit diagram, possibly due to the difficulty in reading this.\n", "\n", "As an example, we see some specific cases of the U-gate in which it is equivalent to the H-gate and P-gate respectively.\n", "\n", "$$\n", "\\begin{aligned}\n", "U(\\tfrac{\\pi}{2}, 0, \\pi) = \\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & 1 \\\\\n", " 1 & -1\n", " \\end{bmatrix} = H\n", "& \\quad &\n", "U(0, 0, \\lambda) = \\begin{bmatrix} 1 & 0 \\\\\n", " 0 & e^{i\\lambda}\\\\\n", " \\end{bmatrix} = P\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHMAAABOCAYAAAATpymVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAFGElEQVR4nO2dbWxTVRjHf22p26AIzAYKAzbLtuoaOll5mR+0TMUAMb4lGhchcRKmc0QzSPwkidGkMTCDBgNGY8TEZIbhFIyLCcjaYEDDGOHV0CkvY7KxIStbWR1bNz8sTgsdVNLuXk6f38dzz33O//bX86S9TVvD0NDQEIISGLUOICQOkakQIlMhRKZCiEyFEJkKITIVQmQqhMhUCJGpECJTIUSmQohMhRCZCiEyFUJkKoTIVAiRqRAiUyFEpkKITIUQmQohMhVCZCqEyFQIkakQIlMhxmkdYKw5tRd6OrROMczEqeB4JHH1Uk5mTwcEW7VOkRykzSqEyFQIkakQIlMhRGacrPDmsOfQl3GPa4HIVAiRqRAiUyF0J3NwcJDq6mry8vJIT0+nsLAQv9+Pw+GgvLxc63i6Rnd3gFatWkVdXR3r16/H7Xazf/9+SktL6ezsZO3atZrlMpnMDAz23zA+EOlnnMmsQaIb0ZXMmpoatm3bhs/nw+PxAFBSUkJTUxN1dXUUFRVpls02JYcLl36LGgv3hejqaWf6PXaNUkWjqzbr9XpZunTpiMh/yM3NxWw243K5NEoGj89/ifpfPuHY6X1EBiP09HaxZecb5Njmkjtjnma5/otudmZrayvHjx+nqqrqhmMtLS04nU7S0tI0SDbMo0Uv0tffy+ZvKrkYPEfGXRZcdg/vvvwdJpM+HkZ9pGBYJoDNZosaD4fD+P1+li1bFlcdg8Fw0+PVrzZQOGfxbWVcvmg1yxetvq1zY+H3+1hQWnLTOf/n1/B002atVisAgUAganzDhg20tbXhdru1iHVHoZudabfbcblceL1eMjMzycrKYseOHdTX1wPELfNWz+TGr/TzeabHs5ihrYn7HUrd7Eyj0UhtbS1Op5OKigrKysqwWq1UVlZiMpk0ffFzp6CbnQmQn59PQ0ND1NjKlSspKCggIyNDo1R3DrqSGYvGxkaKi4vHZK1LV/5gu28jJfNK+XhXFQaDEcesBVQ8uWnUc7buqiLQ2khuVhGVT304JjlHQzdtNhahUIhAIDBmNwsOBXbjzl/CtMnZbHxlLx9U/kQw1MGZtmMx5ze3NhHuC7HptX0MDFzj1PmDY5JzNHS9My0WC5FIJCm1j/zu4+0vnsE+vZD2y2eYM+MBJo7PZM3Tm8lIs4zMMxnNGI2mmDV+bfkZd/4SAIryHuPkuQM4Zi2Ia613ynYm/Jp0vTOTydx7H8YxayHvV/hw2T28/uwW/rp2NUrk6QtHuXK1k+xpBTFrhMJBxqfdDcCE9EmEwsG410oGKSuz7fJppmcO31PtvHKeYKgT+4zCkePdvZf56Ns1rHvus1FrTEifRG9fNwBX+7qxZEyOay3rpKwEXUU0KSvzXPsJsm1OIoMRDAYjTc27cecNt8xIZID3alZQ/kQ1mXfbRsa6ei5G1SjIfpDDzT8CcLh5D/fPLo457/q1kkXKyjx78QQ505z0D/QRDHXQ1LyH/JnzAfAfrSVw/iCffv8m67Yu5uTZA7R3neXzH96KqpE3swizOZ2qLQ9hNJq4b/bCmPOuX+vP7rakXJMh1f4KY7Q7QP4j2/EUPj/qefuOfo1l/BTm5d78+wTxzgOYPBPmv3DLaXEjMjUk0TJTts2qiK7fZyaDiVO1TvAvic6Scm1WZaTNKoTIVAiRqRAiUyFEpkKITIUQmQohMhVCZCqEyFQIkakQIlMhRKZCiEyFEJkKITIVQmQqhMhUiL8B0eiSJErCcAQAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's have U-gate transform a |0> to |+> state\n", "qc = QuantumCircuit(1)\n", "qc.u(pi/2, 0, pi, 0)\n", "qc.draw('mpl')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "state = sim.run(qobj).result().get_statevector()\n", "plot_bloch_multivector(state)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It should be obvious from this that there are an infinite number of possible gates, and that this also includes Rx and Ry-gates, although they are not mentioned here. It must also be noted that there is nothing special about the Z-basis, except that it has been selected as the standard computational basis. Qiskit also provides the X equivalent of the S and Sdg-gate i.e. the SX-gate and SXdg-gate respectively. These gates do a quarter-turn with respect to the X-axis around the Block sphere and are a special case of the Rx-gate.\n", "\n", "\n", "Before running on real IBM quantum hardware, all single-qubit operations are compiled down to $I$ , $X$, $SX$ and $R_{z}$ . For this reason they are sometimes called the _physical gates_.\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Quantum Measurements\n", "\n", "### Part 1: Measuring the state of a qubit\n", "\n", "
\n", "
\n", "

Goal

\n", "

Determine the Bloch components of a qubit.

\n", "
\n", "\n", "Fundamental to the operation of a quantum computer is the ability to compute the Bloch components of a qubit or qubits. These components correspond to the expectation values of the Pauli operators $X, Y, Z$, and are important quantities for applications such as quantum chemistry and optimization. Unfortunately, it is impossible to simultaneously compute these values, thus requiring many executions of the same circuit. In addition, measurements are restricted to the computational basis (Z-basis) so that each Pauli needs to be rotated to the standard basis to access the x and y components. Here we verify the methods by considering the case of a random vector on the Bloch sphere." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from qiskit import *\n", "import numpy as np\n", "from numpy import linalg as la\n", "from qiskit.tools.monitor import job_monitor\n", "import qiskit.tools.jupyter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1. Express the expectation values of the Pauli operators for an arbitrary qubit state $|q\\rangle$ in the computational basis.\n", "\n", "The case for the expectation value of Pauli Z gate is given as an example. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the diagonal representation, also known as spectral form or orthonormal decomposition, of Pauli $Z$ gate and the relations among the Pauli gates (see [here](https://qiskit.org/textbook/ch-states/single-qubit-gates.html)), expectation values of $ X, Y, Z $ gates can be written as \n", "\n", "$$\n", "\\begin{align}\n", "\\langle Z \\rangle &=\\langle q | Z | q\\rangle =\\langle q|0\\rangle\\langle 0|q\\rangle - \\langle q|1\\rangle\\langle 1|q\\rangle\n", "=|\\langle 0 |q\\rangle|^2 - |\\langle 1 | q\\rangle|^2\\\\\\\\\n", "\\langle X \\rangle &= \\\\\\\\\n", "\\langle Y \\rangle &=\n", "\\end{align}\n", "\\\\\n", "$$\n", ", respectively.\n", "\n", "Therefore, the expectation values of the Paulis for a qubit state $|q\\rangle$ can be obtained by making a measurement in the standard basis after rotating the standard basis frame to lie along the corresponding axis. The probabilities of obtaining the two possible outcomes 0 and 1 are used to evaluate the desired expectation value as the above equations show." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2. Measure the Bloch sphere coordinates of a qubit using the Aer simulator and plot the vector on the Bloch sphere." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step A. Create a qubit state using the circuit method, initialize with two random complex numbers as the parameter.\n", "\n", "To learn how to use the function `initialize`, check [here](https://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html#Arbitrary-initialization). (go to the `arbitrary initialization` section.)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "qc = QuantumCircuit(1, 1)\n", "\n", "#### your code goes here\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step B. Build the circuits to measure the expectation values of $X, Y, Z$ gate based on your answers to the question 1. Run the cell below to estimate the Bloch sphere coordinates of the qubit from step A using the Aer simulator.\n", "\n", "The circuit for $Z$ gate measurement is given as an example." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "ename": "QiskitError", "evalue": "'No counts for experiment \"0\"'", "output_type": "error", "traceback": [ "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", "\u001B[0;31mQiskitError\u001B[0m Traceback (most recent call last)", "Input \u001B[0;32mIn [15]\u001B[0m, in \u001B[0;36m\u001B[0;34m()\u001B[0m\n\u001B[1;32m 28\u001B[0m \u001B[38;5;28;01mfor\u001B[39;00m measure_circuit \u001B[38;5;129;01min\u001B[39;00m [measure_x, measure_y, measure_z]:\n\u001B[1;32m 29\u001B[0m \n\u001B[1;32m 30\u001B[0m \u001B[38;5;66;03m# run the circuit with the selected measurement and get the number of samples that output each bit value\u001B[39;00m\n\u001B[1;32m 31\u001B[0m circ_trans \u001B[38;5;241m=\u001B[39m transpile(qc\u001B[38;5;241m.\u001B[39mcompose(measure_circuit), sim)\n\u001B[0;32m---> 32\u001B[0m counts \u001B[38;5;241m=\u001B[39m \u001B[43msim\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mrun\u001B[49m\u001B[43m(\u001B[49m\u001B[43mqc\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mcompose\u001B[49m\u001B[43m(\u001B[49m\u001B[43mcirc_trans\u001B[49m\u001B[43m)\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mshots\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mshots\u001B[49m\u001B[43m)\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mresult\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mget_counts\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 34\u001B[0m \u001B[38;5;66;03m# calculate the probabilities for each bit value\u001B[39;00m\n\u001B[1;32m 35\u001B[0m probs \u001B[38;5;241m=\u001B[39m {}\n", "File \u001B[0;32m~/Prog/miniconda3/envs/qiskit/lib/python3.8/site-packages/qiskit/result/result.py:300\u001B[0m, in \u001B[0;36mResult.get_counts\u001B[0;34m(self, experiment)\u001B[0m\n\u001B[1;32m 298\u001B[0m dict_list\u001B[38;5;241m.\u001B[39mappend(statevector\u001B[38;5;241m.\u001B[39mStatevector(vec)\u001B[38;5;241m.\u001B[39mprobabilities_dict(decimals\u001B[38;5;241m=\u001B[39m\u001B[38;5;241m15\u001B[39m))\n\u001B[1;32m 299\u001B[0m \u001B[38;5;28;01melse\u001B[39;00m:\n\u001B[0;32m--> 300\u001B[0m \u001B[38;5;28;01mraise\u001B[39;00m QiskitError(\u001B[38;5;124mf\u001B[39m\u001B[38;5;124m'\u001B[39m\u001B[38;5;124mNo counts for experiment \u001B[39m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;132;01m{\u001B[39;00m\u001B[38;5;28mrepr\u001B[39m(key)\u001B[38;5;132;01m}\u001B[39;00m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124m'\u001B[39m)\n\u001B[1;32m 302\u001B[0m \u001B[38;5;66;03m# Return first item of dict_list if size is 1\u001B[39;00m\n\u001B[1;32m 303\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mlen\u001B[39m(dict_list) \u001B[38;5;241m==\u001B[39m \u001B[38;5;241m1\u001B[39m:\n", "\u001B[0;31mQiskitError\u001B[0m: 'No counts for experiment \"0\"'" ] } ], "source": [ "# z measurement of qubit 0\n", "measure_z = QuantumCircuit(1,1)\n", "measure_z.measure(0,0)\n", "\n", "# x measurement of qubit 0\n", "measure_x = QuantumCircuit(1,1)\n", "# your code goes here\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "# y measurement of qubit 0\n", "measure_y = QuantumCircuit(1,1)\n", "# your code goes here\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "shots = 2**14 # number of samples used for statistics\n", "sim = Aer.get_backend('aer_simulator')\n", "bloch_vector_measure = []\n", "for measure_circuit in [measure_x, measure_y, measure_z]:\n", " \n", " # run the circuit with the selected measurement and get the number of samples that output each bit value\n", " circ_trans = transpile(qc.compose(measure_circuit), sim)\n", " counts = sim.run(qc.compose(circ_trans), shots=shots).result().get_counts()\n", "\n", " # calculate the probabilities for each bit value\n", " probs = {}\n", " for output in ['0','1']:\n", " if output in counts:\n", " probs[output] = counts[output]/shots\n", " else:\n", " probs[output] = 0\n", " \n", " bloch_vector_measure.append( probs['0'] - probs['1'] )\n", "\n", "# normalizing the Bloch sphere vector\n", "bloch_vector = bloch_vector_measure/la.norm(bloch_vector_measure)\n", "\n", "print('The Bloch sphere coordinates are [{0:4.3f}, {1:4.3f}, {2:4.3f}]'\n", " .format(*bloch_vector)) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step C. Plot the vector on the Bloch sphere.\n", "\n", "Note that the following cell for the interactive bloch_sphere would not run properly unless you work in [IQX](https://quantum-computing.ibm.com/login). You can either use `plot_bloch_vector` for the non-interactive version or install `kaleidoscope` by running \n", "\n", "```\n", "pip install kaleidoscope\n", "\n", "```\n", "in a terminal. You also need to restart your kernel after the installation. To learn more about how to use the interactive Bloch sphere, go [here](https://nonhermitian.org/kaleido/stubs/kaleidoscope.interactive.bloch_sphere.html#kaleidoscope.interactive.bloch_sphere)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from kaleidoscope.interactive import bloch_sphere\n", "\n", "bloch_sphere(bloch_vector, vectors_annotation=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.visualization import plot_bloch_vector\n", "\n", "plot_bloch_vector( bloch_vector )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part 2: Measuring Energy\n", "\n", "
\n", "
\n", "

Goal

\n", "

Evaluate the energy levels of the hydrogen ground state using Aer simulator.

\n", "
\n", "\n", "\n", "The energy of a quantum system can be estimated by measuring the expectation value of its Hamiltonian, which is a Hermitian operator, through the procedure we mastered in part 1.\n", "\n", "The ground state of hydrogen is not defined as a single unique state but actually contains four different states due to the spins of the electron and proton. In part 2 of this lab, we evaluate the energy difference among these four states, which is from the `hyperfine splitting`, by computing the energy expectation value for the system of two spins with the Hamiltonian expressed in Pauli operators. For more information about `hyperfine structure`, see [here](https://www.feynmanlectures.caltech.edu/III_12.html)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the system with two qubit interaction Hamiltonian $H = A(XX+YY+ZZ)$ where $A = 1.47e^{-6} eV$ and $X, Y, Z$ are Pauli gates. Then the energy expectation value of the system can be evaluated by combining the expectation value of each term in the Hamiltonian.\n", "In this case, $E = \\langle H\\rangle = A( \\langle XX\\rangle + \\langle YY\\rangle + \\langle ZZ\\rangle )$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1. Express the expectation value of each term in the Hamiltonian for an arbitrary two qubit state $|\\psi \\rangle$ in the computational basis.\n", "\n", "The case for the term $\\langle ZZ\\rangle$ is given as an example.\n", "\n", "$$\n", "\\begin{align}\n", "\\langle ZZ\\rangle &=\\langle \\psi | ZZ | \\psi\\rangle =\\langle \\psi|(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|)\\otimes(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|) |\\psi\\rangle\n", "=|\\langle 00|\\psi\\rangle|^2 - |\\langle 01 | \\psi\\rangle|^2 - |\\langle 10 | \\psi\\rangle|^2 + |\\langle 11|\\psi\\rangle|^2\\\\\\\\\n", "\\langle XX\\rangle &= \\\\\\\\\n", "\\langle YY\\rangle &=\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2. Measure the expected energy of the system using the Aer simulator when two qubits are entangled. Regard the bell basis, four different entangled states." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step A. Construct the circuits to prepare four different bell states.\n", "\n", "Let's label each bell state as\n", "$$\n", "\\begin{align}\n", "Tri1 &= \\frac{1}{\\sqrt2} (|00\\rangle + |11\\rangle)\\\\\n", "Tri2 &= \\frac{1}{\\sqrt2} (|00\\rangle - |11\\rangle)\\\\\n", "Tri3 &= \\frac{1}{\\sqrt2} (|01\\rangle + |10\\rangle)\\\\\n", "Sing &= \\frac{1}{\\sqrt2} (|10\\rangle - |01\\rangle)\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# circuit for the state Tri1\n", "Tri1 = QuantumCircuit(2, 2)\n", "# your code goes here\n", "\n", "\n", "\n", "\n", "\n", "\n", "# circuit for the state Tri2\n", "Tri2 = QuantumCircuit(2, 2)\n", "# your code goes here\n", "\n", "\n", "\n", "\n", "\n", "# circuit for the state Tri3\n", "Tri3 = QuantumCircuit(2, 2)\n", "# your code goes here\n", "\n", "\n", "\n", "\n", "\n", "\n", "# circuit for the state Sing\n", "Sing = QuantumCircuit(2, 2)\n", "# your code goes here\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step B. Create the circuits to measure the expectation value of each term in the Hamiltonian based on your answer to the question 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# \n", "measure_ZZ = QuantumCircuit(2)\n", "measure_ZZ.measure_all()\n", "\n", "# \n", "measure_XX = QuantumCircuit(2)\n", "# your code goes here\n", "\n", "\n", "\n", "\n", "\n", "# \n", "measure_YY = QuantumCircuit(2)\n", "# your code goes here\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " ##### Step C. Execute the circuits on Aer simulator by running the cell below and evaluate the energy expectation value for each state." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "shots = 2**14 # number of samples used for statistics\n", "\n", "A = 1.47e-6 #unit of A is eV\n", "E_sim = []\n", "for state_init in [Tri1,Tri2,Tri3,Sing]:\n", " Energy_meas = []\n", " for measure_circuit in [measure_XX, measure_YY, measure_ZZ]:\n", " \n", " # run the circuit with the selected measurement and get the number of samples that output each bit value\n", " qc = state_init.compose(measure_circuit)\n", " qc_trans = transpile(qc, sim)\n", " counts = sim.run(qc_trans, shots=shots).result().get_counts()\n", "\n", " # calculate the probabilities for each computational basis\n", " probs = {}\n", " for output in ['00','01', '10', '11']:\n", " if output in counts:\n", " probs[output] = counts[output]/shots\n", " else:\n", " probs[output] = 0\n", " \n", " Energy_meas.append( probs['00'] - probs['01'] - probs['10'] + probs['11'] )\n", " \n", " E_sim.append(A * np.sum(np.array(Energy_meas)))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Run this cell to print out your results\n", "\n", "print('Energy expectation value of the state Tri1 : {:.3e} eV'.format(E_sim[0]))\n", "print('Energy expectation value of the state Tri2 : {:.3e} eV'.format(E_sim[1]))\n", "print('Energy expectation value of the state Tri3 : {:.3e} eV'.format(E_sim[2]))\n", "print('Energy expectation value of the state Sing : {:.3e} eV'.format(E_sim[3]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " ##### Step D. Understanding the result.\n", "\n", "If you found the energy expectation values successfully, you would have obtained exactly the same value, $A (= 1.47e^{-6} eV)$, for the triplet states, $|Tri1\\rangle, |Tri2\\rangle, |Tri3\\rangle$ and one lower energy level, $-3A (= -4.41e^{-6} eV)$ for the singlet state $|Sing\\rangle$. \n", "\n", "What we have done here is measuring the energies of the four different spin states corresponding to the ground state of hydrogen and observed `hyperfine structure` in the energy levels caused by spin-spin coupling. This tiny energy difference between the singlet and triplet states is the reason for the famous 21-cm wavelength radiation used to map the structure of the galaxy. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the cell below, we verify the wavelength of the emission from the transition between the triplet states and singlet state. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# reduced plank constant in (eV) and the speed of light(cgs units)\n", "hbar, c = 4.1357e-15, 3e10\n", "\n", "# energy difference between the triplets and singlet\n", "E_del = abs(E_sim[0] - E_sim[3])\n", "\n", "# frequency associated with the energy difference\n", "f = E_del/hbar\n", "\n", "# convert frequency to wavelength in (cm) \n", "wavelength = c/f\n", "\n", "print('The wavelength of the radiation from the transition\\\n", " in the hyperfine structure is : {:.1f} cm'.format(wavelength))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part 3: Execute the circuits on Quantum Computer\n", "\n", "
\n", "
\n", "

Goal

\n", "

Re-run the circuits on a IBM quantum system. Perform measurement error mitigations on the result to improve the accuracy in the energy estimation.

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step A. Run the following cells to load your account and select the backend" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "provider = IBMQ.load_account()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "backend = provider.get_backend('ibm_lima')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step B. Execute the circuits on the quantum system.\n", "\n", "\n", "In Lab1 when we executed multiple circuits on a real quantum system, we submitted each circuit as a separate job which produces the multiple job ids. This time, we put all the circuits in a list and execute the list of the circuits as one job. In this way, all the circuit executions can happen at once, which would possibly decrease your wait time in the queue." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

📓 Check the backend configuration information and error map through the widget to determine your initial_layout." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "# run this cell to get the backend information through the widget\n", "backend" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "# assign your choice for the initial layout to the list variable `initial_layout`.\n", "initial_layout = " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the following cell to execute the circuits with the initial_layout on the backend." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "qc_all = [state_init.compose(measure_circuit) for state_init in [Tri1,Tri2,Tri3,Sing] \n", " for measure_circuit in [measure_XX, measure_YY, measure_ZZ] ] \n", "\n", "shots = 8192\n", "qc_all_trans = transpile(qc_all, backend, initial_layout=initial_layout, optimization_level=3)\n", "job = backend.run(qc_all_trans, shots=shots)\n", "print(job.job_id())" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "# getting the results of your job\n", "results = job.result()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "## To access the results of the completed job\n", "#results = backend.retrieve_job('job_id').result()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step C. Estimate the ground state energy levels from the results of the previous step by executing the cells below." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "def Energy(results, shots):\n", " \"\"\"Compute the energy levels of the hydrogen ground state.\n", " \n", " Parameters:\n", " results (obj): results, results from executing the circuits for measuring a Hamiltonian.\n", " shots (int): shots, number of shots used for the circuit execution.\n", " \n", " Returns:\n", " Energy (list): energy values of the four different hydrogen ground states\n", " \"\"\"\n", " E = []\n", " A = 1.47e-6\n", "\n", " for ind_state in range(4):\n", " Energy_meas = []\n", " for ind_comp in range(3):\n", " counts = results.get_counts(ind_state*3+ind_comp)\n", " \n", " # calculate the probabilities for each computational basis\n", " probs = {}\n", " for output in ['00','01', '10', '11']:\n", " if output in counts:\n", " probs[output] = counts[output]/shots\n", " else:\n", " probs[output] = 0\n", " \n", " Energy_meas.append( probs['00'] - probs['01'] - probs['10'] + probs['11'] )\n", "\n", " E.append(A * np.sum(np.array(Energy_meas)))\n", " \n", " return E" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "E = Energy(results, shots)\n", "\n", "print('Energy expectation value of the state Tri1 : {:.3e} eV'.format(E[0]))\n", "print('Energy expectation value of the state Tri2 : {:.3e} eV'.format(E[1]))\n", "print('Energy expectation value of the state Tri3 : {:.3e} eV'.format(E[2]))\n", "print('Energy expectation value of the state Sing : {:.3e} eV'.format(E[3]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step D. Measurement error mitigation.\n", "\n", "The results you obtained from running the circuits on the quantum system are not exact due to the noise from the various sources such as enery relaxation, dephasing, crosstalk between qubits, etc. In this step, we will alleviate the effects of the noise through the measurement error mitigation. Before we start, watch this [video](https://www.youtube.com/watch?v=yuDxHJOKsVA&list=PLOFEBzvs-Vvp2xg9-POLJhQwtVktlYGbY&index=8). " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.ignis.mitigation.measurement import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

📓Construct the circuits to profile the measurement errors of all basis states using the function 'complete_meas_cal'. Obtain the measurement filter object, 'meas_filter', which will be applied to the noisy results to mitigate readout (measurement) error.

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For further helpful information to complete this task, check [here](https://qiskit.org/textbook/ch-quantum-hardware/measurement-error-mitigation.html) . " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# your code to create the circuits, meas_calibs, goes here\n", "meas_calibs, state_labels = \n", "\n", "\n", "\n", "# execute meas_calibs on your choice of the backend\n", "meas_calibs_trans = transpile(meas_calibs, backend, optimization_level=3)\n", "job = backend.run(meas_calibs_trans, backend, shots = shots)\n", "print(job.job_id())\n", "job_monitor(job)\n", "cal_results = job.result()\n", "\n", "## To access the results of the completed job\n", "#cal_results = backend.retrieve_job('job_id').result()\n", "\n", "\n", "# your code to obtain the measurement filter object, 'meas_filter', goes here\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "results_new = meas_filter.apply(results)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "E_new = Energy(results_new, shots)\n", "\n", "print('Energy expection value of the state Tri1 : {:.3e} eV'.format(E_new[0]))\n", "print('Energy expection value of the state Tri2 : {:.3e} eV'.format(E_new[1]))\n", "print('Energy expection value of the state Tri3 : {:.3e} eV'.format(E_new[2]))\n", "print('Energy expection value of the state Sing : {:.3e} eV'.format(E_new[3]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Step E. Interpret the result." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

📓 Compute the relative errors ( or the fractional error ) of the energy values for all four states with and without measurement error mitigation.

" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# results for the energy estimation from the simulation, \n", "# execution on a quantum system without error mitigation and\n", "# with error mitigation in numpy array format \n", "Energy_exact, Energy_exp_orig, Energy_exp_new = np.array(E_sim), np.array(E), np.array(E_new)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Calculate the relative errors of the energy values without error mitigation \n", "# and assign to the numpy array variable `Err_rel_orig` of size 4\n", "Err_rel_orig = " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Calculate the relative errors of the energy values with error mitigation \n", "# and assign to the numpy array variable `Err_rel_new` of size 4\n", "Err_rel_new = " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.set_printoptions(precision=3)\n", "\n", "print('The relative errors of the energy values for four bell basis\\\n", " without measurement error mitigation : {}'.format(Err_rel_orig))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.set_printoptions(precision=3)\n", "\n", "print('The relative errors of the energy values for four bell basis\\\n", " with measurement error mitigation : {}'.format(Err_rel_new))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

📓 Compare the size of the errors before and after the measurment error mitigation and discuss about the effect of the readout error regarding the error map information of the backend that you selected.

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Your answer:**" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Using your IBM credentials locally\n", "\n", "The IBM Quantum account has functions for handling administrative tasks. The credentials can be saved to disk, or used in a session and never saved.\n", "\n", "* `enable_account(TOKEN, HUB, GROUP, PROJECT)`: Enable your account in the current session and optionally specify a default provider to return.\n", "* `save_account(TOKEN, HUB, GROUP, PROJECT)`: Save your account to disk for future use, and optionally specify a default provider to return when loading your account.\n", "* `load_account()`: Load account using stored credentials.\n", "* `disable_account()`: Disable your account in the current session.\n", "* `stored_account()`: List the account stored to disk.\n", "* `active_account()`: List the account currently in the session.\n", "* `delete_account()`: Delete the saved account from disk.\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "from qiskit import IBMQ,visualization\n", "# Enter your token from the IBM cloud here for temporary activation (I have mine saved, so not necessary)\n", "#if IBMQ.active_account() == None :\n", "# print(\"Enabling saved account\")\n", "# IBMQ.enable_account(\"your token here\")\n", "### If you have used save_account beforehand, you can load it here\n", "if (IBMQ.active_account() is None) and (IBMQ.stored_account() is not None) :\n", " print(\"Loading saved account\")\n", " provider = IBMQ.load_account()\n", "#\n", "#print(\"Currently active account:\", IBMQ.active_account())" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "As a part of the education problem, probably you have access to at least two providers." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[,\n", " ,\n", " ]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "IBMQ.providers() # List all available providers" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Let's select the `hub='ibm-q-education', group='mid-east-tech-un-1'` (since it has more resources, and less wait time). Each provider provides access to a number of _backends_ i.e. quantum computers." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# If you have access to more than one hub:\n", "provider = IBMQ.get_provider(hub='ibm-q-education', group='mid-east-tech-un-1')\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Currently, there is a SDK change in Qiskit preventing us selecting a backend automatically. Let's select one using the \"IBM Q Services\" page by selecting \"Your Systems\"" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "97631da5b8af4781a8fd05ff5de85eb1", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(HTML(value=\"

" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "backend=provider.get_backend('ibm_perth')\n", "backend" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "One important aspect of the devices is what is called the \"qubit topology\"\n", "\n", "The graph below shows you how the physical qubits are connected together on the real device you will be using. For example, on the graph, qubit 0 has a physical connection to qubit 1 and qubit 3 has connections to 1 and 5 on the quantum device but qubit 0 is not connected directly to 2\n", "\n", "This graph is really important when Qiskit tries to map a circuit to the quantum device because it shows how qubits are connected and this is a huge step in transforming circuits to run in devices. For example, since 0 and 1 are connected, it will have no problem executing a C-NOT between the two. But if you wish to do the same between 0 and 2, this will be harder because of the lack of connection.\n", "\n", "The process of rewriting circuits is what we call transpilation. Without it, we won't be able to run circuits on quantum devices. This will be explained later in the class" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "visualization.plot_gate_map(backend)\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Each quantum computer has different characteristics. Remember, it is not just the number of qubit, but also how the qubits are connected matters. You can check the topologies in the IBM Q webpage" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Qiskit Visualization tools\n", "\n", "Within the physics community, the qubits of a multi-qubit systems are typically ordered with the first qubit on the left-most side of the tensor product and the last qubit on the right-most side. For instance, if the first qubit is in state $ \\left|0\\right\\rangle $ and second is in state $ \\left|1\\right\\rangle $, their joint state would be $ \\left|01\\right\\rangle $. Qiskit uses a slightly different ordering of the qubits, in which the qubits are represented from the most significant bit (MSB) on the left to the least significant bit (LSB) on the right (big-endian). This is similar to bitstring representation on classical computers, and enables easy conversion from bitstrings to integers after measurements are performed. For the example just given, the joint state would be represented as $ \\left|10\\right\\rangle $.\n", "\n", "Importantly, this change in the representation of multi-qubit states affects the way multi-qubit gates are represented in Qiskit, as discussed [here](htps://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html#Two-qubit-gates_)\n", "\n", "The representation used in Qiskit enumerates the basis vectors in increasing order of the integers they represent. For instance, the basis vectors for a 2-qubit system would be ordered as $ \\left|00\\right\\rangle$, $ \\left|01\\right\\rangle $, $ \\left|10\\right\\rangle $, and $ \\left|11\\right\\rangle $. Thinking of the basis vectors as bit strings, they encode the integers 0,1,2 and 3, respectively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have already seen how to plot the results in a histogram. There are other visualization tools that are useful when working with quantum computers, let's explore them.\n", "\n", "### Plot a state\n", "\n", "In many situations you want to see the state of a quantum computer. This could be for debugging. Here we assume you have this state (either from simulation or state tomography) and the goal is to visualize the quantum state. This requires exponential resources, so we advise to only view the state of small quantum systems. There are several functions for generating different types of visualization of a quantum state\n", "\n", "\n", "\n", "```\n", "plot_state_city(quantum_state)\n", "plot_state_qsphere(quantum_state)\n", "plot_state_paulivec(quantum_state)\n", "plot_state_hinton(quantum_state)\n", "plot_bloch_multivector(quantum_state)\n", "```\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A quantum state is either a state matrix $ \\rho $ (Hermitian matrix) or statevector $ \\left|\\psi\\right\\rangle $ (complex vector). The state matrix is related to the statevector by\n", "$$ \\rho = \\left| \\psi \\right\\rangle\\!\\left\\langle \\psi \\right| $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The visualizations generated by the functions are:\n", "\n", "`'plot_state_city'`: The standard view for quantum states where the real and imaginary (imag) parts of the state matrix are plotted like a city.\n", "\n", "`'plot_state_qsphere'`: The Qiskit unique view of a quantum state where the amplitude and phase of the state vector are plotted in a spherical ball. \n", "The amplitude is the thickness of the arrow and the phase is the color. For mixed states it will show different 'qsphere' for each component.\n", "\n", "`'plot_state_paulivec'`: The representation of the state matrix using Pauli operators as the basis. \n", "\n", "`'plot_state_hinton'`: Same as 'city' but where the size of the element represents the value of the matrix element.\n", "\n", "`'plot_bloch_multivector'`: The projection of the quantum state onto the single qubit space and plotting on a bloch sphere." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.visualization import plot_state_city, plot_bloch_multivector\n", "from qiskit.visualization import plot_state_paulivec, plot_state_hinton\n", "from qiskit.visualization import plot_state_qsphere" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "circuit = QuantumCircuit(2, 2)\n", "circuit.h(0)\n", "circuit.cx(0, 1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "backend = Aer.get_backend('statevector_simulator') # the device to run on\n", "result = backend.run(circuit).result()\n", "psi = result.get_statevector(circuit)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plot_state_city(psi)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plot_state_hinton(psi)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plot_state_qsphere(psi)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plot_state_paulivec(psi)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plot_bloch_multivector(psi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plot Bloch Vector\n", "\n", "A standard way of plotting a quantum system is using the Bloch vector. This only works for a single qubit and takes as input the Bloch vector." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.visualization import plot_bloch_vector" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plot_bloch_vector([0,1,0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Circuit Visualization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When building a quantum circuit, it often helps to draw the circuit. This is supported natively by a ``QuantumCircuit`` object. You can either call ``print()`` on the circuit, or call the ``draw()`` method on the object." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Build a quantum circuit\n", "circuit = QuantumCircuit(3, 3)\n", "\n", "circuit.x(1)\n", "circuit.h(range(3))\n", "circuit.cx(0, 1)\n", "circuit.measure(range(3), range(3));" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(circuit)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "circuit.draw(output='mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are different drawing formats. The parameter output (str) selects the output method to use for drawing the circuit. Valid choices are ``text, mpl, latex, latex_source``. See [qiskit.circuit.QuantumCircuit.draw](https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.draw.html?highlight=draw)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "circuit.draw(initial_state=True, output='mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Depending on the output, there are also options to customize the circuit diagram rendered by the circuit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Disable Plot Barriers and Reversing Bit Order" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first two options are shared among all three backends. They allow you to configure both the bit orders and whether or not you draw barriers. These can be set by the ``reverse_bits`` `kwarg and ``plot_barriers`` kwarg, respectively. The examples below will work with any output backend; mpl is used here for brevity." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Draw a new circuit with barriers and more registers\n", "\n", "q_a = QuantumRegister(3, name='qa')\n", "q_b = QuantumRegister(5, name='qb')\n", "c_a = ClassicalRegister(3)\n", "c_b = ClassicalRegister(5)\n", "\n", "circuit = QuantumCircuit(q_a, q_b, c_a, c_b)\n", "\n", "circuit.x(q_a[1])\n", "circuit.x(q_b[1])\n", "circuit.x(q_b[2])\n", "circuit.x(q_b[4])\n", "circuit.barrier()\n", "circuit.h(q_a)\n", "circuit.barrier(q_a)\n", "circuit.h(q_b)\n", "circuit.cswap(q_b[0], q_b[1], q_b[2])\n", "circuit.cswap(q_b[2], q_b[3], q_b[4])\n", "circuit.cswap(q_b[3], q_b[4], q_b[0])\n", "circuit.barrier(q_b)\n", "circuit.measure(q_a, c_a)\n", "circuit.measure(q_b, c_b);" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Draw the circuit\n", "circuit.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Draw the circuit with reversed bit order\n", "circuit.draw(output='mpl', reverse_bits=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Draw the circuit without barriers\n", "circuit.draw(output='mpl', plot_barriers=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Backend specific costumizations" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Change the background color in mpl\n", "\n", "style = {'backgroundcolor': 'lightgreen'}\n", "\n", "circuit.draw(output='mpl', style=style)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Scale the mpl output to 1/2 the normal size\n", "circuit.draw(output='mpl', scale=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also use ``circuit_drawer()`` as a function" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.tools.visualization import circuit_drawer" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "circuit_drawer(circuit, output='mpl', plot_barriers=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulators " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will show how to import the Qiskit Aer simulator backend and use it to run ideal (noise free) Qiskit Terra circuits." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# Import Qiskit\n", "from qiskit import QuantumCircuit\n", "from qiskit import Aer, transpile\n", "from qiskit.tools.visualization import plot_histogram, plot_state_city\n", "import qiskit.quantum_info as qi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Aer provider contains a variety of high performance simulator backends for a variety of simulation methods. The available backends on the current system can be viewed using ``Aer.backends``" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "Aer.backends()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The main simulator backend of the Aer provider is the ``AerSimulator`` backend. A new simulator backend can be created using ``Aer.get_backend('aer_simulator')``." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "simulator = Aer.get_backend('aer_simulator')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The default behavior of the ``AerSimulator`` backend is to mimic the execution of an actual device. If a ``QuantumCircuit`` containing measurements is run it will return a count dictionary containing the final values of any classical registers in the circuit. The circuit may contain gates, measurements, resets, conditionals, and other custom simulator instructions " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create circuit\n", "circ = QuantumCircuit(2)\n", "circ.h(0)\n", "circ.cx(0, 1)\n", "circ.measure_all()\n", "\n", "# Transpile for simulator\n", "simulator = Aer.get_backend('aer_simulator')\n", "circ = transpile(circ, simulator)\n", "\n", "# Run and get counts\n", "result = simulator.run(circ).result()\n", "counts = result.get_counts(circ)\n", "plot_histogram(counts, title='Bell-State counts')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Run and get memory (measurement outcomes for each individual shot)\n", "result = simulator.run(circ, shots=10, memory=True).result()\n", "memory = result.get_memory(circ)\n", "print(memory)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Simulation methods\n", "\n", "The AerSimulator supports a variety of simulation methods, each of which supports a different set of instructions. The method can be set manually using ``simulator.set_option(method=value)`` option, or a simulator backend with a preconfigured method can be obtained directly from the Aer provider using ``Aer.get_backend``.\n", "\n", "When simulating ideal circuits, changing the method between the exact simulation methods stabilizer, ``statevector``, ``density_matrix`` and ``matrix_product_state`` should not change the simulation result (other than usual variations from sampling probabilities for measurement outcomes)\n", "\n", "Each of these methods determines the internal representation of the quantum circuit and the algorithms used to process the quantum operations. They each have advantages and disadvantages, and choosing the best method is a matter of investigation. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Increase shots to reduce sampling variance\n", "shots = 10000\n", "\n", "# Stabilizer simulation method\n", "sim_stabilizer = Aer.get_backend('aer_simulator_stabilizer')\n", "job_stabilizer = sim_stabilizer.run(circ, shots=shots)\n", "counts_stabilizer = job_stabilizer.result().get_counts(0)\n", "\n", "# Statevector simulation method\n", "sim_statevector = Aer.get_backend('aer_simulator_statevector')\n", "job_statevector = sim_statevector.run(circ, shots=shots)\n", "counts_statevector = job_statevector.result().get_counts(0)\n", "\n", "# Density Matrix simulation method\n", "sim_density = Aer.get_backend('aer_simulator_density_matrix')\n", "job_density = sim_density.run(circ, shots=shots)\n", "counts_density = job_density.result().get_counts(0)\n", "\n", "# Matrix Product State simulation method\n", "sim_mps = Aer.get_backend('aer_simulator_matrix_product_state')\n", "job_mps = sim_mps.run(circ, shots=shots)\n", "counts_mps = job_mps.result().get_counts(0)\n", "\n", "plot_histogram([counts_stabilizer, counts_statevector, counts_density, counts_mps],\n", " title='Counts for different simulation methods',\n", " legend=['stabilizer', 'statevector',\n", " 'density_matrix', 'matrix_product_state'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The default simulation method is automatic which will automatically select a one of the other simulation methods for each circuit based on the instructions in those circuits. A fixed simulation method can be specified by by adding the method name when getting the backend, or by setting the method option on the backend." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### GPU simulation\n", "\n", "The statevector, density_matrix and unitary simulators support running on a NVidia GPUs. For these methods the simulation device can also be manually set to CPU or GPU using ``simulator.set_options(device='GPU')`` backend option. If a GPU device is not available setting this option will raise an exception." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.providers.aer import AerError\n", "\n", "# Initialize a GPU backend\n", "\n", "try:\n", " simulator_gpu = Aer.get_backend('aer_simulator')\n", " simulator_gpu.set_options(device='GPU')\n", "except AerError as e:\n", " print(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Aer provider will also contain preconfigured GPU simulator backends if Qiskit Aer was installed with GPU support on a compatible system::\n", "\n", "* ``aer_simulator_statevector_gpu``\n", "* ``aer_simulator_density_matrix_gpu``\n", "* ``aer_simulator_unitary_gpu``\n", "\n", "Note: The GPU version of Aer can be installed using ``pip install qiskit-aer-gpu``." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Simulation precision\n", "\n", "One of the available simulator options allows setting the float precision for the statevector, density_matrix unitary and superop methods. This is done using the ``set_precision=\"single\"`` or ``precision=\"double\" `` (default) option:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Configure a single-precision statevector simulator backend\n", "simulator = Aer.get_backend('aer_simulator_statevector')\n", "simulator.set_options(precision='single')\n", "\n", "# Run and get counts\n", "result = simulator.run(circ).result()\n", "counts = result.get_counts(circ)\n", "print(counts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Setting the simulation precision applies to both CPU and GPU simulation devices. Single precision will halve the required memory and may provide performance improvements on certain systems." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Can we simulate noise?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Device backend noise model simulations\n", "\n", "We will now show how to use the Qiskit Aer noise module to automatically generate a basic noise model for an IBMQ hardware device, and use this model to do noisy simulations of QuantumCircuits to study the effects of errors which occur on real devices.\n", "\n", "Note, that these automatic models are only an approximation of the real errors that occur on actual devices, due to the fact that they must be build from a limited set of input parameters related to average error rates on gates. The study of quantum errors on real devices is an active area of research and we discuss the Qiskit Aer tools for configuring more detailed noise models in another notebook." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit import IBMQ, transpile\n", "from qiskit import QuantumCircuit\n", "from qiskit.providers.aer import AerSimulator\n", "from qiskit.tools.visualization import plot_histogram" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Qiskit Aer device noise model automatically generates a simplified noise model for a real device. This model is generated using the calibration information reported in the ``BackendProperties`` of a device and takes into account\n", "\n", "* The gate_error probability of each basis gate on each qubit.\n", "* The gate_length of each basis gate on each qubit.\n", "* The T1, T2 relaxation time constants of each qubit.\n", "* The readout error probability of each qubit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use real noise data for an IBM Quantum device using the data stored in Qiskit Terra. Specifically, in this tutorial, the device is ``ibmq_vigo```." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.test.mock import FakeVigo\n", "device_backend = FakeVigo()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we construct a test circuit to compare the output of the real device with the noisy output simulated on the Qiskit Aer AerSimulator. Before running with noise or on the device we show the ideal expected output with no noise." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct quantum circuit\n", "circ = QuantumCircuit(3, 3)\n", "circ.h(0)\n", "circ.cx(0, 1)\n", "circ.cx(1, 2)\n", "circ.measure([0, 1, 2], [0, 1, 2])\n", "\n", "sim_ideal = AerSimulator()\n", "\n", "# Execute and get counts\n", "result = sim_ideal.run(transpile(circ, sim_ideal)).result()\n", "counts = result.get_counts(0)\n", "plot_histogram(counts, title='Ideal counts for 3-qubit GHZ state')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How to generate a simulator that mimics a device?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We call ``from_backend`` to create a simulator for ``ibmq_vigo``" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sim_vigo = AerSimulator.from_backend(device_backend)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By storing the device properties in ``vigo_simulator``, we ensure that the appropriate basis gates and coupling map are used when compiling circuits for simulation, thereby most closely mimicking the gates that will be executed on a real device. In addition ``vigo_simulator`` contains an approximate noise model consisting of:\n", "\n", "* Single-qubit gate errors consisting of a single qubit depolarizing error followed by a single qubit thermal relaxation error.\n", "* Two-qubit gate errors consisting of a two-qubit depolarizing error followed by single-qubit thermal relaxation errors on both qubits in the gate.\n", "* Single-qubit readout errors on the classical bit value obtained from measurements on individual qubits.\n", "\n", "For the gate errors the error parameter of the thermal relaxation errors is derived using the ``thermal_relaxation_error`` function from ``aer.noise.errors module``, along with the individual qubit T1 and T2 parameters, and the ``gate_time`` parameter from the device backend properties. The probability of the depolarizing error is then set so that the combined average gate infidelity from the depolarizing error followed by the thermal relaxation is equal to the ``gate_error`` value from the backend properties.\n", "\n", "For the readout errors the probability that the recorded classical bit value will be flipped from the true outcome after a measurement is given by the qubit ``readout_errors``." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once we have created a noisy simulator backend based on a real device we can use it to run noisy simulations.\n", "\n", "Important: When running noisy simulations it is critical to transpile the circuit for the backend so that the circuit is transpiled to the correct noisy basis gate set for the backend." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Transpile the circuit for the noisy basis gates\n", "tcirc = transpile(circ, sim_vigo)\n", "\n", "# Execute noisy simulation and get counts\n", "result_noise = sim_vigo.run(tcirc).result()\n", "counts_noise = result_noise.get_counts(0)\n", "plot_histogram(counts_noise,\n", " title=\"Counts for 3-qubit GHZ state with device noise model\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may also be interested in:\n", "* Building Noise Models https://qiskit.org/documentation/tutorials/simulators/3_building_noise_models.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Applying noise to custom unitary gates https://qiskit.org/documentation/tutorials/simulators/4_custom_gate_noise.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Introduction to Quantum Gates and Circuits. Building Circuits with multiple components." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Quantum Circuit Properties" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When constructing quantum circuits, there are several properties that help quantify the “size” of the circuits, and their ability to be run on a noisy quantum device. Some of these, like number of qubits, are straightforward to understand, while others like depth and number of tensor components require a bit more explanation. Here we will explain all of these properties, and, in preparation for understanding how circuits change when run on actual devices, highlight the conditions under which they change." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "qc = QuantumCircuit(12)\n", "for idx in range(5):\n", " qc.h(idx)\n", " qc.cx(idx, idx+5)\n", "\n", "qc.cx(1, 7)\n", "qc.x(8)\n", "qc.cx(1, 9)\n", "qc.x(7)\n", "qc.cx(1, 11)\n", "qc.swap(6, 11)\n", "qc.swap(6, 9)\n", "qc.swap(6, 10)\n", "qc.x(6)\n", "qc.draw(output=\"mpl\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the plot, it is easy to see that this circuit has 12 qubits, and a collection of Hadamard, CNOT, X, and SWAP gates. But how to quantify this programmatically? Because we can do single-qubit gates on all the qubits simultaneously, the number of qubits in this circuit is equal to the width of the circuit:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "qc.width()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also just get the number of qubits directly:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "qc.num_qubits" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**IMPORTANT**\n", "\n", "For a quantum circuit composed from just qubits, the circuit width is equal to the number of qubits. This is the definition used in quantum computing. However, for more complicated circuits with classical registers, and classically controlled gates, this equivalence breaks down. As such, from now on we will not refer to the number of qubits in a quantum circuit as the width\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is also straightforward to get the number and type of the gates in a circuit using `QuantumCircuit.count_ops()`:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "qc.count_ops()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also get just the raw count of operations by computing the circuits `QuantumCircuit.size()`:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "qc.size()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A particularly important circuit property is known as the circuit depth. The depth of a quantum circuit is a measure of how many “layers” of quantum gates, executed in parallel, it takes to complete the computation defined by the circuit. Because quantum gates take time to implement, the depth of a circuit roughly corresponds to the amount of time it takes the quantum computer to execute the circuit. Thus, the depth of a circuit is one important quantity used to measure if a quantum circuit can be run on a device." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "qc.depth()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Final Statevector and Unitary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To save the final statevector of the simulation we can append the circuit with the ``save_statevector`` instruction. Note that this instruction should be applied before any measurements if we do not want to save the collapsed post-measurement state" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Saving the final statevector\n", "# Construct quantum circuit without measure\n", "\n", "from qiskit.visualization import array_to_latex\n", "\n", "circuit = QuantumCircuit(2)\n", "circuit.h(0)\n", "circuit.cx(0, 1)\n", "circuit.save_statevector()\n", "\n", "backend = Aer.get_backend('aer_simulator')\n", "result = backend.run(circuit).result()\n", "array_to_latex(result.get_statevector())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To save the unitary matrix for a ``QuantumCircuit`` we can append the circuit with the ``save_unitary`` instruction. Note that this circuit cannot contain any measurements or resets since these instructions are not supported on for the ``\"unitary\"`` simulation method" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Saving the circuit unitary\n", "# Construct quantum circuit without measure\n", "\n", "circuit = QuantumCircuit(2)\n", "circuit.h(0)\n", "circuit.cx(0, 1)\n", "circuit.save_unitary()\n", "\n", "result = backend.run(circuit).result()\n", "array_to_latex(result.get_unitary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also apply save instructions at multiple locations in a circuit. Note that when doing this we must provide a unique label for each instruction to retrieve them from the results." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Saving multiple states\n", "# Construct quantum circuit without measure\n", "\n", "steps = 5\n", "circ = QuantumCircuit(1)\n", "for i in range(steps):\n", " circ.save_statevector(label=f'psi_{i}')\n", " circ.rx(i * np.pi / steps, 0)\n", "circ.save_statevector(label=f'psi_{steps}')\n", "\n", "# Transpile for simulator\n", "simulator = Aer.get_backend('aer_simulator')\n", "circ = transpile(circ, simulator)\n", "\n", "# Run and get saved data\n", "result = simulator.run(circ).result()\n", "data = result.data(0)\n", "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Setting a custom statevector\n", "\n", "The ``set_statevector`` instruction can be used to set a custom Statevector state. The input statevector must be valid." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Generate a random statevector\n", "num_qubits = 2\n", "psi = qi.random_statevector(2 ** num_qubits, seed=100)\n", "\n", "# Set initial state to generated statevector\n", "circ = QuantumCircuit(num_qubits)\n", "circ.set_statevector(psi)\n", "circ.save_state()\n", "\n", "# Transpile for simulator\n", "simulator = Aer.get_backend('aer_simulator')\n", "circ = transpile(circ, simulator)\n", "\n", "# Run and get saved data\n", "result = simulator.run(circ).result()\n", "result.data(0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Initialization (Using the initialize instruction)\n", "\n", "qc = QuantumCircuit(4)\n", "\n", "qc.initialize('01+-')\n", "qc.draw()\n", "qc.decompose().draw(output=\"mpl\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Initialization\n", "\n", "import math\n", "\n", "desired_vector = [1 / math.sqrt(2), 1 / math.sqrt(2), 0, 0]\n", "display(array_to_latex(desired_vector))\n", "\n", "\n", "qc = QuantumCircuit(2)\n", "qc.initialize(desired_vector, [0, 1])\n", "qc.draw(output=\"mpl\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit import transpile\n", "simulator = Aer.get_backend('aer_simulator')\n", "qc_transpiled = transpile(qc, simulator, basis_gates=['x', 'cx', 'ry', 'rz'], optimization_level=3)\n", "#qc_transpiled = transpile(qc, simulator, optimization_level=3)\n", "#qc_transpiled.decompose().decompose().decompose().decompose().draw()\n", "qc_transpiled.draw(output=\"mpl\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is another option to initalize the circuit to a desired quantum state. \n", "We use ` qiskit.circuit.QuantumCircuit.isometry` In general, it is used for attaching an arbitrary isometry from m to n qubits to a circuit. In particular, this allows to attach arbitrary unitaries on n qubits (m=n) or to prepare any state on n qubits (m=0). The decomposition used here was introduced by Iten et al. in https://arxiv.org/abs/1501.06911. This is important because in many experimental architectures, the C-NOT gate is relatively 'expensive' and hence we aim to keep the number of these as low as possible. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Isometry\n", "qc = QuantumCircuit(2)\n", "qc.isometry(desired_vector, q_input=[],q_ancillas_for_output=[0,1])\n", "qc.draw(output=\"mpl\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "simulator = Aer.get_backend('aer_simulator')\n", "qc_transpiled = transpile(qc, simulator, optimization_level=3)\n", "qc_transpiled.draw(output=\"mpl\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's compare both circuit outputs. Which one has more gates?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Other components" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#Composite gates\n", "\n", "# Build a sub-circuit\n", "sub_q = QuantumRegister(2)\n", "sub_circ = QuantumCircuit(sub_q, name='sub_circ')\n", "sub_circ.h(sub_q[0])\n", "sub_circ.crz(1, sub_q[0], sub_q[1])\n", "sub_circ.barrier()\n", "sub_circ.id(sub_q[1])\n", "sub_circ.u(1, 2, -2, sub_q[0])\n", "\n", "# Convert to a gate and stick it into an arbitrary place in the bigger circuit\n", "sub_inst = sub_circ.to_instruction()\n", "\n", "qr = QuantumRegister(3, 'q')\n", "circ = QuantumCircuit(qr)\n", "circ.h(qr[0])\n", "circ.cx(qr[0], qr[1])\n", "circ.cx(qr[1], qr[2])\n", "circ.append(sub_inst, [qr[1], qr[2]])\n", "\n", "circ.draw(output=\"mpl\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Circuits are not immediately decomposed upon conversion to_instruction to allow circuit design at higher levels of abstraction. When desired, or before compilation, sub-circuits will be decomposed via the decompose method." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "decomposed_circ = circ.decompose() # Does not modify original circuit\n", "decomposed_circ.draw(output=\"mpl\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Circuit with Global Phase\n", "\n", "circuit = QuantumCircuit(2)\n", "circuit.h(0)\n", "#circuit.save_unitary()\n", "circuit.cx(0, 1)\n", "circuit.global_phase = np.pi / 2\n", "circuit.save_unitary()\n", "\n", "display(circuit.draw(output=\"mpl\"))\n", "#backend = Aer.get_backend('unitary_simulator')\n", "backend = Aer.get_backend('aer_simulator_unitary')\n", "result = backend.run(circuit).result()\n", "array_to_latex(result.get_unitary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Parameterized Quantum Circuits \n", "\n", "from qiskit.circuit import Parameter\n", "theta = Parameter('theta')\n", "\n", "circuit = QuantumCircuit(1)\n", "circuit.rx(theta, 0)\n", "circuit.measure_all()\n", "circuit.draw(output=\"mpl\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sim = Aer.get_backend('aer_simulator')\n", "res = sim.run(circuit, parameter_binds=[{theta: [np.pi/2, np.pi, 0]}]).result() # Different bindings\n", "res.get_counts()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.circuit import Parameter\n", "\n", "theta = Parameter('θ')\n", "\n", "n = 5\n", "\n", "qc = QuantumCircuit(5, 1)\n", "\n", "qc.h(0)\n", "for i in range(n-1):\n", " qc.cx(i, i+1)\n", "\n", "qc.barrier()\n", "qc.rz(theta, range(5))\n", "qc.barrier()\n", "\n", "for i in reversed(range(n-1)):\n", " qc.cx(i, i+1)\n", "qc.h(0)\n", "qc.measure(0, 0)\n", "\n", "qc.draw('mpl')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#We can inspect the circuit’s parameters\n", "print(qc.parameters)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All circuit parameters must be bound before sending the circuit to a backend. This can be done as follows: - The``bind_parameters`` method accepts a dictionary mapping ``Parameter``s to values, and returns a new circuit with each parameter replaced by its corresponding value. Partial binding is supported, in which case the returned circuit will be parameterized by any ``Parameter``s that were not mapped to a value." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "theta_range = np.linspace(0, 2 * np.pi, 128)\n", "\n", "circuits = [qc.bind_parameters({theta: theta_val})\n", " for theta_val in theta_range]\n", "\n", "circuits[-1].draw('mpl')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "backend = Aer.get_backend('aer_simulator')\n", "job = backend.run(transpile(circuits, backend))\n", "counts = job.result().get_counts()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the example circuit, we apply a global Rz(θ) rotation on a five-qubit entangled state, and so expect to see oscillation in qubit-0 at 5θ." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "fig = plt.figure(figsize=(8,6))\n", "ax = fig.add_subplot(111)\n", "\n", "ax.plot(theta_range, list(map(lambda c: c.get('0', 0), counts)), '.-', label='0')\n", "ax.plot(theta_range, list(map(lambda c: c.get('1', 0), counts)), '.-', label='1')\n", "\n", "ax.set_xticks([i * np.pi / 2 for i in range(5)])\n", "ax.set_xticklabels(['0', r'$\\frac{\\pi}{2}$', r'$\\pi$', r'$\\frac{3\\pi}{2}$', r'$2\\pi$'], fontsize=14)\n", "ax.set_xlabel('θ', fontsize=14)\n", "ax.set_ylabel('Counts', fontsize=14)\n", "ax.legend(fontsize=14)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Random Circuit\n", "\n", "from qiskit.circuit.random import random_circuit\n", "\n", "circ = random_circuit(2, 2, measure=True)\n", "circ.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Pauli\n", "from qiskit.quantum_info.operators import Pauli\n", "\n", "circuit = QuantumCircuit(4)\n", "IXYZ = Pauli('IXYZ')\n", "circuit.append(IXYZ, [0, 1, 2, 3])\n", "circuit.draw('mpl')\n", "# circuit.decompose().draw()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Pauli with phase \n", "from qiskit.quantum_info.operators import Pauli\n", "\n", "circuit = QuantumCircuit(4)\n", "iIXYZ = Pauli('iIXYZ') # ['', '-i', '-', 'i']\n", "circuit.append(iIXYZ, [0, 1, 2, 3])\n", "circuit.draw('mpl')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Any unitary!\n", "matrix = [[0, 0, 0, 1],\n", " [0, 0, 1, 0],\n", " [1, 0, 0, 0],\n", " [0, 1, 0, 0]]\n", " \n", "circuit = QuantumCircuit(2)\n", "circuit.unitary(matrix, [0, 1])\n", "circuit.draw('mpl')\n", "# circuit.decompose().draw() #synthesis" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Classical logic\n", "from qiskit.circuit import classical_function, Int1\n", "\n", "@classical_function\n", "def oracle(x: Int1, y: Int1, z: Int1) -> Int1:\n", " return not x and (y or z)\n", "\n", "circuit = QuantumCircuit(4)\n", "circuit.append(oracle, [0, 1, 2, 3])\n", "circuit.draw('mpl')\n", "# circuit.decompose().draw() #synthesis" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Classical logic\n", "from qiskit.circuit import classical_function, Int1\n", "@classical_function\n", "def oracle(x: Int1) -> Int1:\n", " return not x\n", "circuit = QuantumCircuit(2)\n", "circuit.append(oracle, [0, 1])\n", "circuit.draw('mpl')\n", "# circuit.decompose().draw() #synthesis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Run on real hardware. Compiling Circuits\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The backends we have access to" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# If you have access to more than one hub:\n", "provider = IBMQ.get_provider(hub='ibm-q-education', group='mid-east-tech-un-1')\n", "[(b.name(), b.configuration().n_qubits) for b in provider.backends()]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from qiskit.tools.jupyter import *\n", "backend = provider.get_backend('ibm_perth')\n", "backend" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "Not working at the moment\n", "#from qiskit.providers.ibmq import least_busy\n", "#\n", "#backend = least_busy(provider.backends(\n", "# simulator=False,\n", "# filters=lambda b: b.configuration().n_qubits >= 2))\n", "#backend" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's go back to Bell state" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "circuit = QuantumCircuit(2)\n", "circuit.h(0)\n", "circuit.cx(0, 1)\n", "circuit.measure_all()\n", "circuit.draw('mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remember how to run it in a simulator?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sim = Aer.get_backend('aer_simulator')\n", "result = sim.run(circuit).result()\n", "counts = result.get_counts()\n", "plot_histogram(counts)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%qiskit_job_watcher\n", "job = backend.run(circuit)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "job.result()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "circuit.draw('mpl')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit import transpile\n", "\n", "transpiled_circuit = transpile(circuit, backend)\n", "transpiled_circuit.draw('mpl')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "job = backend.run(transpiled_circuit)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "job.status()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "result = job.result()\n", "counts = result.get_counts()\n", "plot_histogram(counts)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.visualization import plot_circuit_layout, plot_gate_map\n", "\n", "display(transpiled_circuit.draw(idle_wires=False))\n", "display(plot_gate_map(backend))\n", "plot_circuit_layout(transpiled_circuit, backend)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# a slightly more interesting example:\n", "circuit = QuantumCircuit(3)\n", "circuit.h([0,1,2])\n", "circuit.ccx(0, 1, 2)\n", "circuit.h([0,1,2])\n", "circuit.ccx(2, 0, 1)\n", "circuit.h([0,1,2])\n", "circuit.measure_all()\n", "circuit.draw()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit, backend)\n", "transpiled.draw(idle_wires=False, fold=-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initial layout" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit, backend, initial_layout=[0, 2, 3])\n", "display(plot_circuit_layout(transpiled, backend))\n", "plot_gate_map(backend)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled.draw(idle_wires=False, fold=-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimization level\n", "\n", "Higher levels generate more optimized circuits, at the expense of longer transpilation time.\n", "\n", " * 0: no explicit optimization other than mapping to backend\n", " * 1: light optimization by simple adjacent gate collapsing.(default)\n", " * 2: medium optimization by noise adaptive qubit mapping and gate cancellation using commutativity rules.\n", " * 3: heavy optimization by noise adaptive qubit mapping and gate cancellation using commutativity rules and unitary synthesis." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "level0 = transpile(circuit, backend, optimization_level=0)\n", "level1 = transpile(circuit, backend, optimization_level=1)\n", "level2 = transpile(circuit, backend, optimization_level=2)\n", "level3 = transpile(circuit, backend, optimization_level=3)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "for level in [level0, level1, level2, level3]:\n", " print(level.count_ops()['cx'], level.depth())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transpiling is a stochastic process" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit, backend, optimization_level=2, seed_transpiler=0)\n", "transpiled.depth()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit, backend, optimization_level=2, seed_transpiler=1)\n", "transpiled.depth()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Playing with other transpiler options (without a backend)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit)\n", "transpiled.draw(fold=-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set a basis gates" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "backend.configuration().basis_gates" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit, basis_gates=['x', 'cx', 'h', 'p'])\n", "transpiled.draw(fold=-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set a coupling map" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "backend.configuration().coupling_map" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit.transpiler import CouplingMap\n", "\n", "transpiled = transpile(circuit, coupling_map=CouplingMap([(0,1),(1,2)]))\n", "transpiled.draw(fold=-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set an initial layout in a coupling map" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit,\n", " coupling_map=CouplingMap([(0,1),(1,2)]),\n", " initial_layout=[1, 0, 2])\n", "transpiled.draw(fold=-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set an initial_layout in the coupling map with basis gates" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit,\n", " coupling_map=CouplingMap([(0,1),(1,2)]),\n", " initial_layout=[1, 0, 2],\n", " basis_gates=['x', 'cx', 'h', 'p']\n", " )\n", "transpiled.draw(fold=-1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled.count_ops()['cx']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plus optimization level" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit,\n", " coupling_map=CouplingMap([(0,1),(1,2)]),\n", " initial_layout=[1, 0, 2],\n", " basis_gates=['x', 'cx', 'h', 'p'],\n", " optimization_level=3\n", " )\n", "transpiled.draw(fold=-1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled.count_ops()['cx']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Last parameter, approximation degree" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit,\n", " coupling_map=CouplingMap([(0,1),(1,2)]),\n", " initial_layout=[1, 0, 2],\n", " basis_gates=['x', 'cx', 'h', 'p'],\n", " approximation_degree=0.99,\n", " optimization_level=3\n", " )\n", "transpiled.draw(fold=-1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled.depth()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled = transpile(circuit,\n", " coupling_map=CouplingMap([(0,1),(1,2)]),\n", " initial_layout=[1, 0, 2],\n", " basis_gates=['x', 'cx', 'h', 'p'],\n", " approximation_degree=0.01,\n", " optimization_level=3\n", " )\n", "transpiled.draw(fold=-1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "transpiled.depth()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Qiskit is hardware agnostic! For example, you can try out trapped ion machines in IONQ https://ionq.com/get-started/#cloud-access" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "!pip install qiskit-ionq" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from qiskit_ionq import IonQProvider\n", "provider = IonQProvider()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "[(b.name(), b.configuration().n_qubits) for b in provider.backends()]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "circuit = QuantumCircuit(2)\n", "circuit.h(0)\n", "circuit.cx(0, 1)\n", "circuit.measure_all()\n", "circuit.draw()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "backend = provider.get_backend(\"ionq_qpu\")\n", "job = backend.run(circuit)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plot_histogram()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "job.get_counts()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plot_histogram(job.get_counts())" ] }, { "cell_type": "markdown", "id": "a245ebab", "metadata": { "collapsed": false }, "source": [ "\n", "\n", "## Quantum Coin Game\n", "\n", "Please check [Ted talk by Sohini Ghosh](https://www.ted.com/talks/shohini_ghose_a_beginner_s_guide_to_quantum_computing#t-208006) and Quantum Coin Flipping from [Wikipedia](https://en.wikipedia.org/wiki/Quantum_coin_flipping) first.\n", "\n", "Quantum Coin Game is one of the fundamental concept of quantum computing, which uses simple implementation of quantum gates or more precisely uses the wierdness of quantum mechanics, to win about 97% of the time, when played against an opponent. Flipping of coin and say heads or tails. The concept of Quantum Coin Game came from the idea of classical coin game which can only show heads and tails. But since the game utilizes the concepts of quantum mechanics, it would be interesting to see what could be the outcome of the whole experiment. The main concept of this game is how the quantum computer uses the power of quantum superposition, which tells an object can exists in 2 different states at the same time, to win absolutely everytime.\n", "\n", " ### What are the rules of this game ?\n", " 1. Quantum Computer plays a move but it is not revealed to the Opponent(Human).\n", " 2. Opponent(Human) plays a move and it is also not revealed to the Quantum Computer.\n", " 3. Finally Quantum Computer plays a move.\n", " 4. Results are shown. If its heads, then Quantum Computer wins. Else, Opponent(Human) wins.\n", "\n", "**NOTE**: \"Playing a move\" refers to \"Flipping the coin\" and we consider the coin as fair coin.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "b8474d7b", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "d3219e82a0fd4ca1b8d5ee149522628d", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(Dropdown(description='Choice: ', options=(('Identity', 'i'), ('Bit Flip', 'x')), value='i'), Bu…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Importing all the necessary library\n", "from qiskit import QuantumCircuit, Aer, IBMQ, QuantumRegister, ClassicalRegister, execute\n", "from qiskit.tools.jupyter import *\n", "from qiskit.visualization import *\n", "import qiskit.tools.jupyter\n", "import ipywidgets as widgets\n", "\n", "# Layout\n", "button_p = widgets.Button(\n", " description='Play')\n", "gate_p = widgets.Dropdown(\n", " options=[('Identity', 'i'), ('Bit Flip', 'x')],\n", " description='Choice: ',\n", " disabled=False,\n", ")\n", "out_p = widgets.Output()\n", "def on_button_clicked(b):\n", " with out_p:\n", " \n", " # Initial Circuit\n", " circuit_p = QuantumRegister(1, 'circuit')\n", " measure_p = ClassicalRegister(1, 'result')\n", " qc_p = QuantumCircuit(circuit_p, measure_p)\n", " \n", " # Turn 1\n", " qc_p.h(circuit_p[0])\n", " \n", " # Turn 2\n", " if gate_p.value == 'i':\n", " qc_p.i(circuit_p[0])\n", " if gate_p.value == 'x':\n", " qc_p.x(circuit_p[0])\n", " \n", " # Turn 3\n", " qc_p.h(circuit_p[0])\n", " \n", " # Measure \n", " qc_p.measure(circuit_p, measure_p)\n", " \n", " # QASM\n", " backend_p = Aer.get_backend('aer_simulator')\n", " job_p = execute(qc_p, backend_p, shots=8192)\n", " res_p = job_p.result().get_counts()\n", " \n", " # Result\n", " if len(res_p) == 1 and list(res_p.keys())[0] == '0':\n", " print(\"You Lose to Quantum. Quantum Computer Wins\")\n", " if len(res_p) == 1 and list(res_p.keys())[0] == '1':\n", " print(\"You Win against Quantum Computer\")\n", " if len(res_p) == 2:\n", " print(\"Either Quantum or You Wins\")\n", "\n", "button_p.on_click(on_button_clicked)\n", "widgets.VBox([gate_p, button_p, out_p])" ] }, { "cell_type": "markdown", "id": "a7cbcd28", "metadata": { "id": "TMsXKAxk6-dt" }, "source": [ "### Analogy\n", "\n", "Now that we know what is a quantum coin game, what is it based on and most importantly what are the rules of this game, lets convert the concept of this game in quantum computing terminology.\n", "\n", "* The 'coin' in flipping a coin we referring here is a 'single qubit gate'.\n", "\n", "$$\n", " |\\psi\\rangle=\\begin{bmatrix}\\alpha \\\\ \\beta\\end{bmatrix}\n", "$$\n", "\n", " where $\\alpha, \\beta \\in \\mathbb{C}$ and $|\\alpha|^2 + |\\beta|^2 = 1$\n", "\n", "\n", "* \"Flipping\" the coin is application of the bit-flip operator\n", "\n", "$$\n", " X = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix}\n", "$$\n", "\n", "* The \"heads\" state is defined as \n", "$$\n", "|0\\rangle = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\n", "$$ and \"tails\" as \n", "$$\n", "|1\\rangle = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\n", "$$\n", "\n", "* The quantum computer \"plays\" by applying the Hadamard $H$ operator \n", "$$\n", "H = \\frac{1}{\\sqrt{2}} \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", "$$\n" ] }, { "cell_type": "markdown", "id": "14066634", "metadata": { "id": "PdPizFWxBr5m" }, "source": [ "### Approach\n", "\n", "Lets see how to approach the game in quantum computing terminology-\n", "\n", "* The coin is initialized to the $|0\\rangle$ \"heads\" state.\n", "\n", "* The computer plays, applying the Hadamard $H$ operator to the coin (operators are applied using matrix multiplication). \n", "$$\n", "H|0\\rangle = \\frac{1}{\\sqrt2}(|0\\rangle + |1\\rangle)\n", "$$\n", "The coin enters the \n", "$$\n", "H|0\\rangle = |+\\rangle = \\frac{1}{\\sqrt{2}} \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix}\n", "$$\n", "state.\n", "\n", "\n", "* The human plays, choosing whether to flip the coin (apply the $X$ operator) or do nothing (apply the $I$ operator). However, since the $X$ operator just flips the state vector upside down, $X$ has no effect. Same goes for $I$.\n", "$$\n", "X|+\\rangle=|+\\rangle \n", "$$\n", "$$\n", "I|+\\rangle=|+\\rangle \n", "$$\n", "No matter what, the state is $|+\\rangle$ after the human plays.\n", "\n", "* The computer plays, applying the Hadamard $H$ operator again, taking the coin to the $|0⟩$ \"heads\" state.\n", "$$\n", "H|+\\rangle = |0\\rangle\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "id": "aa5a026d", "metadata": { "id": "mEDO89d8L1pG" }, "outputs": [], "source": [ "# Importing all the necessary library\n", "\n", "from qiskit import QuantumCircuit, Aer, IBMQ, QuantumRegister, ClassicalRegister, execute\n", "from qiskit.tools.jupyter import *\n", "from qiskit.visualization import *\n", "import qiskit.tools.jupyter\n", "import ipywidgets as widgets" ] }, { "cell_type": "code", "execution_count": 4, "id": "5c132150", "metadata": {}, "outputs": [], "source": [ "# Building the initial circuit\n", "\n", "def initial_circuit():\n", " circuit = QuantumRegister(1, 'circuit')\n", " measure = ClassicalRegister(1, 'result')\n", " qc = QuantumCircuit(circuit, measure)\n", " qc.draw('mpl')\n", " return qc, circuit, measure" ] }, { "cell_type": "code", "execution_count": 5, "id": "a0bdf0dc", "metadata": {}, "outputs": [], "source": [ "# Widget Initialization\n", "\n", "gate = widgets.Dropdown(\n", " options=[('Identity', 'i'), ('Bit Flip', 'x')],\n", " description='Choice: ',\n", " disabled=False,\n", ")" ] }, { "cell_type": "markdown", "id": "51292438", "metadata": {}, "source": [ "### Optimal Strategy\n", "\n", "Using the above approach the possibility table reduces to-\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "
Start StateQuantumClassicalQuantumResultWho Wins?
$|0\\rangle$$H$$I$$H$$|0\\rangle$Quantum
$|0\\rangle$$H$$X$$H$$|0\\rangle$Quantum
\n", "\n", "Now lets look at the possibilities-\n", "\n", "\n", "1. Quantum Computer Wins ( $|0\\rangle$ ):\n", "\n", "$$\n", "\\frac{2}{2} = 100 \\%\n", "$$\n", "\n", "2. Classical Human Wins ( $|1\\rangle$ ):\n", "\n", "$$\n", " \\frac{0}{2} = 0 \\%\n", "$$\n", "\n", "3. Either Quantum Computer or Classical Human Wins ( $|0\\rangle + |1\\rangle$ ):\n", "\n", "$$\n", " \\frac{0}{2} = 0 \\%\n", "$$" ] }, { "cell_type": "markdown", "id": "c6ac8039", "metadata": {}, "source": [ "This table shows the quantum computer wins $100\\%$ of the time. But in Shohini's talk it is $~97\\%$, due to errors." ] }, { "cell_type": "markdown", "id": "b3fbf470", "metadata": {}, "source": [ "### Lets play this version using Qiskit" ] }, { "cell_type": "markdown", "id": "e8fa09d1", "metadata": {}, "source": [ "#### Building the initial circuit" ] }, { "cell_type": "code", "execution_count": 6, "id": "1becf96d", "metadata": {}, "outputs": [], "source": [ "qc, circuit, measure = initial_circuit()" ] }, { "cell_type": "markdown", "id": "50761468", "metadata": {}, "source": [ "#### **Turn 1. Quantum Computer**" ] }, { "cell_type": "code", "execution_count": 7, "id": "5b020ed0", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Use H Gate\n", "\n", "qc.h(circuit[0])\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "id": "9460c1ed", "metadata": {}, "source": [ "#### **Turn 2. Classical Human**" ] }, { "cell_type": "code", "execution_count": 8, "id": "9937d190", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "if gate.value == 'i':\n", " qc.i(circuit[0])\n", "if gate.value == 'x':\n", " qc.x(circuit[0])\n", "\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "id": "eaa49c0a", "metadata": {}, "source": [ "#### **Turn 3. Quantum Computer**" ] }, { "cell_type": "markdown", "id": "62201773", "metadata": {}, "source": [ "Quantum Computer uses Hadamard $H$ on its first turn" ] }, { "cell_type": "code", "execution_count": 9, "id": "7871350a", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Used H Gate\n", "\n", "qc.h(circuit[0])\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "id": "0dcf9d65", "metadata": {}, "source": [ "#### **Measurement** " ] }, { "cell_type": "code", "execution_count": 10, "id": "1af614ff", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc.measure(circuit, measure)\n", "qc.draw('mpl')" ] }, { "cell_type": "markdown", "id": "db5bf662", "metadata": {}, "source": [ "#### **QASM_Simulator** " ] }, { "cell_type": "code", "execution_count": 11, "id": "01ec610d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'0': 8192}\n" ] }, { "data": { "image/png": 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QH1N9DNmngYci4qzMfKQ2ZvIAc05uRtGSJO0xZGhm5uLhKGSA714PrK9rWhURxwFfBB7pd6MhRMQCaqsXtbW10dnZCcC0adMYN24c69atA2DChAnMmDGDlStXAjBmzBg6OjpYu3YtO3bsAKBSqdDb2wscvy+lSJKaqKenh/Xrq5ExdepU2tvb6erqAmDs2LFUKhVWrVrFrl27AOjo6GDDhg1s3boVgJkzZ+7tG0hUH1jSmIj4CPAeqj/bPpWZnQXbHEb1gqFLMvOeuva/BmZm5lmF3/2nwMWZ+e7a538Gvp6ZX60b80Xg8sx8xwDTAFCpVLK7u3uwIUXm37LfU0iS9tPSK5szT0SsycxKf30NXQgUEVMjYjXwINXHgX2J6s+lXREx6FNOMnM3sAaY3adrNtWraEudRPVn2z1WNWFOSZKG1Ogyev+F6nM0p2fmswARMQ34Zq3vD4fY/mbgrlrwPgpcRvWRYrfV5loGkJlza5+vBJ4DnqJ6TvNTwAXARXVz3gqsjIgvAd8BPg58GOhocN8kSRpUo6E5G5i1JzABMvOZiFgEPDTUxpl5d20pvqup3m/5JHBuZm6qDel7v+ZhwFeBdmAn1fA8LzOX1835WERcDFxP9baXfwLmZGZXg/smSdKg9mXB9v5OghafGM3MJcCSAfpm9fl8E3BTwZz30ryrfCVJ6lejixs8BHw9Io7Z01BbzecWCo40JUl6M2s0NBcBbwOeiYhNEbGJ6s+hb6v1SZJ00Gr059mfAx8EZgF7Fk3/aWb+n2YWJUlSKyoOzYg4FPgl8L7MfJDqbSeSJI0axT/P1hZJ30T1ilZJkkadRs9p/ifgzyNi4oEoRpKkVtboOc0vUH3KyZaI2EyfZ2tm5onNKkySpFbTaGjeS/WezDgAtUiS1NKKQjMijqC6Ms8FwO9QvSfziszcduBKkySptZSe01wMzAN+APwPqs+//K8HqCZJklpS6c+zFwL/PjP/J0BEfAt4NCIOrV1VK0nSQa/0SPMY6h76nJmrgdeoPqFEkqRRoTQ0DwV292l7jX1b8F2SpDel0tAL4JsRsauu7XBgaUS8vKchM89vZnGSJLWS0tC8s5+2bzazEEmSWl1RaGbmvzvQhUiS1OoaXUZPkqRRy9CUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoNe2hGxGcj4tmIeCUi1kTEGYOMvTAiVkTEixHxq4joiojz+4yZFxHZz+vwA783kqTRZFhDMyLmALcCNwInA48B90XEsQNschbwQ+C82vjlwN/3E7QvA1PqX5n5SvP3QJI0mo0Z5u+7CrgjM5fWPl8REf8aWAh8ue/gzPxcn6bFEXEecAHwyL8cmi8cgHolSdpr2I40I+Iw4APAij5dK4DTG5hqHLC9T9tbI2JTRGyOiO9HxMn7UaokSf0aziPNicChQG+f9l7goyUTRMQfAe3AXXXN64FLgXVUA/VzwKMR8b7M3NjPHAuABQBtbW10dnYCMG3aNMaNG8e6desAmDBhAjNmzGDlypUAjBkzho6ODtauXcuOHTsAqFQq9Pb2AseXlC9JOoB6enpYv349AFOnTqW9vZ2uri4Axo4dS6VSYdWqVezatQuAjo4ONmzYwNatWwGYOXPm3r6BRGYewF2o+6KINmALcFZmrqxrvxb4ZGb+/hDbX0Q1LOdk5vcGGXco8I/Aw5m5aLA5K5VKdnd3l+/EAObfst9TSJL209IrmzNPRKzJzEp/fcN5IdA24HVgUp/2ScCg5yMj4g+pBubcwQITIDNfB7qBE/a9VEmS3mjYQjMzdwNrgNl9umZTvYq2XxHxCaqBOS8z7x3qeyIigBOBnn2vVpKkNxruq2dvBu6KiNXAo8BlQBtwG0BELAPIzLm1zxdTDcwvACsjYnJtnt2Z+VJtzJ8CjwMbgSOBRVRDc+Ew7ZMkaZQY1tDMzLsjYgJwNdX7KZ8Ezs3MTbUhfe/XvIxqjbfUXnv8CJhVe/+7wO3AZOCXwD8AZ2bm6qbvgCRpVBvuI00ycwmwZIC+WYN9HmCbzwOfb0ZtkiQNxrVnJUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQsMemhHx2Yh4NiJeiYg1EXHGEOPPqo17JSKeiYjL9ndOSZL2xbCGZkTMAW4FbgROBh4D7ouIYwcY/05geW3cycBXgK9HxEX7OqckSftquI80rwLuyMylmfnTzLwC6AEWDjD+MuD5zLyiNn4pcCfwhf2YU5KkfTJsoRkRhwEfAFb06VoBnD7AZqf1M/4BoBIRv7OPc0qStE+G80hzInAo0NunvReYPMA2kwcYP6Y2377MKUnSPhkz0gUMt4hYACyoffx1RKwfyXqkFjIR2DbSRUj76m8/37Sp3jFQx3CG5jbgdWBSn/ZJwAsDbPPCAONfq80Xjc6ZmbcDtxdXLY0SEdGdmZWRrkNqZcP282xm7gbWALP7dM2mesVrf1YNML47M1/dxzklSdonw/3z7M3AXRGxGniU6tWxbcBtABGxDCAz59bG3wZcHhG3AH8DfAiYB1xSOqckSc0yrKGZmXdHxATgamAK8CRwbmZuqg05ts/4ZyPiXOAvqd5C8jywKDO/3cCcksp42kIaQmTmSNcgSdKbgmvPSpJUyNCUJKmQoSlJUiFDUxrFIuKEiOh7n7OkAXghkDTKRMTRwKeBzwMvUl0spAe4F/h2Zv5mBMuTWpqhKY0yEXEH8B7g+8DPgQnAScC7gc3ATZn54EjVJ7UyQ1MaRSIigF9RvZd5ZV1bO3AqMJ/quptzMvMfR6pOqVV5TlMaXd4DPAvs3tOQVT/LzHuAf0M1VOeMUH1SSzM0pdHlGWAr8Je1i4D+xb8BtfWc7wTOGYnipFZnaEqjSGbuBP4EeCuwDJgbEcdExFiAiDgCOIvqcpSS+vCcpjQKRcRM4BrgfOA3VJ8o9CLwUapX0n4mM58YuQql1mRoSqNY7faT84ALgFeoHmHek5n/dyTrklqVoSkJgIg4JDN/O9J1SK3M0JQkqZAXAkmSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBX6f7FBpj2rWUTSAAAAAElFTkSuQmCC\n", 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" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "backend = Aer.get_backend('aer_simulator')\n", "job = execute(qc, backend, shots=8192)\n", "res = job.result().get_counts()\n", "print(res)\n", "plot_histogram(res)" ] }, { "cell_type": "markdown", "id": "14223907", "metadata": { "tags": [] }, "source": [ "#### **Lets see who wins** " ] }, { "cell_type": "code", "execution_count": 12, "id": "4f2c0789", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Quantum Computer Wins\n" ] } ], "source": [ "if len(res) == 1 and list(res.keys())[0] == '0':\n", " print(\"Quantum Computer Wins\")\n", "if len(res) == 1 and list(res.keys())[0] == '1':\n", " print(\"Classical Human Wins\")\n", "if len(res) == 2:\n", " print(\"Either Quantum Computer or Classical Human Wins\")" ] }, { "cell_type": "markdown", "id": "a3e5831d", "metadata": { "tags": [] }, "source": [ "#### **Running on Quantum Computer** " ] }, { "cell_type": "code", "execution_count": 13, "id": "308b15a2", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [ { "ename": "IBMQAccountCredentialsNotFound", "evalue": "'No IBM Quantum Experience credentials found.'", "output_type": "error", "traceback": [ "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", "\u001B[0;31mIBMQAccountCredentialsNotFound\u001B[0m Traceback (most recent call last)", "Input \u001B[0;32mIn [13]\u001B[0m, in \u001B[0;36m\u001B[0;34m()\u001B[0m\n\u001B[0;32m----> 1\u001B[0m provider \u001B[38;5;241m=\u001B[39m \u001B[43mIBMQ\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mload_account\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 2\u001B[0m backend_real \u001B[38;5;241m=\u001B[39m provider\u001B[38;5;241m.\u001B[39mget_backend(\u001B[38;5;124m'\u001B[39m\u001B[38;5;124mibmq_manila\u001B[39m\u001B[38;5;124m'\u001B[39m)\n\u001B[1;32m 3\u001B[0m job_real \u001B[38;5;241m=\u001B[39m execute(qc, backend_real, shots\u001B[38;5;241m=\u001B[39m\u001B[38;5;241m8192\u001B[39m)\n", "File \u001B[0;32m~/Prog/miniconda3/envs/QisKit/lib/python3.8/site-packages/qiskit/providers/ibmq/ibmqfactory.py:167\u001B[0m, in \u001B[0;36mIBMQFactory.load_account\u001B[0;34m(self)\u001B[0m\n\u001B[1;32m 164\u001B[0m credentials_list \u001B[38;5;241m=\u001B[39m \u001B[38;5;28mlist\u001B[39m(stored_credentials\u001B[38;5;241m.\u001B[39mvalues())\n\u001B[1;32m 166\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m credentials_list:\n\u001B[0;32m--> 167\u001B[0m \u001B[38;5;28;01mraise\u001B[39;00m IBMQAccountCredentialsNotFound(\n\u001B[1;32m 168\u001B[0m \u001B[38;5;124m'\u001B[39m\u001B[38;5;124mNo IBM Quantum Experience credentials found.\u001B[39m\u001B[38;5;124m'\u001B[39m)\n\u001B[1;32m 170\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mlen\u001B[39m(credentials_list) \u001B[38;5;241m>\u001B[39m \u001B[38;5;241m1\u001B[39m:\n\u001B[1;32m 171\u001B[0m \u001B[38;5;28;01mraise\u001B[39;00m IBMQAccountMultipleCredentialsFound(\n\u001B[1;32m 172\u001B[0m \u001B[38;5;124m'\u001B[39m\u001B[38;5;124mMultiple IBM Quantum Experience credentials found. \u001B[39m\u001B[38;5;124m'\u001B[39m \u001B[38;5;241m+\u001B[39m UPDATE_ACCOUNT_TEXT)\n", "\u001B[0;31mIBMQAccountCredentialsNotFound\u001B[0m: 'No IBM Quantum Experience credentials found.'" ] } ], "source": [ "provider = IBMQ.load_account()\n", "backend_real = provider.get_backend('ibmq_manila')\n", "job_real = execute(qc, backend_real, shots=8192)\n", "res_real = job_real.result().get_counts()\n", "print(res_real)\n", "plot_histogram(res_real)" ] }, { "cell_type": "markdown", "id": "f8be92c9", "metadata": {}, "source": [ "Unlike the perfect simulation, the real quantum computer only wins ~$99\\ \\%$ of the time, the $1\\ \\%$ in which it loses is due to errors. Quantum computers have improved a bit since [Shohini's talk](#conclusion) where the error is closer to $3\\ \\%$." ] }, { "cell_type": "markdown", "id": "52f27e41", "metadata": {}, "source": [ "### Conclusion\n", "\n", "This simple and yet fun little game shows the basic quantum states $|0\\rangle$, $|1\\rangle$, $|+\\rangle$ and $|−\\rangle$, plus the common ways of moving between them with the $X$, $H$, $I$, $Z$ gates." ] }, { "cell_type": "markdown", "id": "a4fc3c5c", "metadata": {}, "source": [ "### Send it after class:\n", "\n", "Think of other variations of the game, and tweak the game as follows\n", "\n", "1. What if, instead of quantum computer taking first turn, the classical human take the first turn ?\n", "2. What if, instead of representing head as $|0\\rangle$, the tail is represented as $|0\\rangle$ ?\n", "3. What if, instead of using fair coin, we used unfair coin ?\n", "4. What if, instead of playing against a classical human, the quantum computer plays with another quantum computer ?\n", "5. What if, instead of having 3 turns, there are $n$ number of turns ?\n", "6. What if, instead of using all gates, restrict the use of some gates ?\n", "\n", "how did the results change?" ] }, { "cell_type": "markdown", "id": "50307881", "metadata": {}, "source": [ "## Local Reality and the CHSH inequality\n", "\n", "We have seen in a previous module how quantum entanglement results in strong correlations in a multi-partite system. In fact these correlations appear to be stronger than anything that could be explained using classical physics.\n", "\n", "The historical development of quantum mechanics is filled with agitated discussions about the true nature of reality and the extent to which quantum mechanics can explain it. Given the spectacular empirical success of quantum mechanics, it was going to be clear that people would not simply give it up just because some of its aspects were hard to reconcile with intuition.\n", "\n", "At the root of these different points of views was the question of the nature of measurement. We know there is an element of randomness in quantum measurements, but is that really so? Is there a sneaky way by which the Universe has already decided beforehand which value a given measurement is going to yield at a future time? This hypothesis was the basis for different _hidden variable_ theories. But these theories did not only need to explain randomness at the single particle level. They also needed to explain what happens when different observers measure different parts of a multi-partite entangled system! This went beyond just hidden variable theories. Now a local hidden variable theory was needed in order to reconcile the observations of quantum mechanics with a Universe in which local reality was valid.\n", "\n", "What is local reality? In an Universe where locality holds, it should be possible to separate two systems so far in space that they could not interact with each other. The concept of reality is related to whether a measurable quantity holds a particular value _in the absence of any future measurement_. \n", "\n", "In 1963, John Stewart Bell published what could be argued as one of the most profound discoveries in the history of science. Bell stated that any theory invoking local hidden variables could be experimentally ruled out. In this section we are going to see how, and we will run a real experiment that demonstrates so! (with some remaining loopholes to close...)" ] }, { "cell_type": "markdown", "id": "393c4477", "metadata": {}, "source": [ "### The CHSH inequality\n", "\n", "Imagine Alice and Bob are given each one part of a bipartite entangled system. Each of them then performs two measurements on their part in two different bases. Let's call Alice's bases _A_ and _a_ and Bob's _B_ and _b_. What is the expectation value of the quantity $\\langle CHSH \\rangle = \\langle AB \\rangle - \\langle Ab \\rangle + \\langle aB \\rangle + \\langle ab \\rangle$ ? \n", "\n", "Now, Alice and Bob have one qubit each, so any measurement they perform on their system (qubit) can only yield one of two possible outcomes: +1 or -1. Note that whereas we typically refer to the two qubit states as $|0\\rangle$ and $|1\\rangle$, these are *eigenstates*, and a projective measurement will yield their *eigenvalues*, +1 and -1, respectively. \n", "\n", "Therefore, if any measurement of _A_, _a_, _B_, and _b_ can only yield $\\pm 1$, the quantities $(B-b)$ and $(B+b)$ can only be 0 or $\\pm2$. And thus, the quantity $A(B-b) + a(B+b)$ can only be either +2 or -2, which means that there should be a bound for the expectation value of the quantity we have called $|\\langle CHSH \\rangle| =|\\langle AB \\rangle - \\langle Ab \\rangle + \\langle aB \\rangle + \\langle ab \\rangle| \\leq 2$.\n", "\n", "Now, the above discussion is oversimplified, because we could consider that the outcome on any set of measurements from Alice and Bob could depend on a set of local hidden variables, but it can be shown with some math that, even when that is the case, the expectation value of the quantity $CHSH$ should be bounded by 2 if local realism held.\n", "\n", "But what happens when we do these experiments with an entangled system? Let's try it!" ] }, { "cell_type": "code", "execution_count": 14, "id": "350a1a98", "metadata": {}, "outputs": [], "source": [ "#import qiskit tools\n", "import qiskit\n", "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, transpile, Aer, IBMQ\n", "from qiskit.tools.visualization import circuit_drawer\n", "from qiskit.tools.monitor import job_monitor, backend_monitor, backend_overview\n", "from qiskit.providers.aer import noise\n", "\n", "#import python stuff\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import time" ] }, { "cell_type": "code", "execution_count": null, "id": "8a084c54", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "# Set devices, if using a real device\n", "IBMQ.load_account()\n", "provider = IBMQ.get_provider('ibm-q')\n", "quito = provider.get_backend('ibmq_quito')" ] }, { "cell_type": "code", "execution_count": null, "id": "5c7a87c7", "metadata": {}, "outputs": [], "source": [ "sim = Aer.get_backend('aer_simulator')" ] }, { "cell_type": "markdown", "id": "a9d70842", "metadata": {}, "source": [ "First we are going to define a function to create our CHSH circuits. We are going to choose, without loss of generality, that Bob always uses the computational ($Z$) and the $X$ bases for his $B$ and $b$ measurements, respectively, whereas Alice chooses also orthogonal bases but whose angle we are going to vary between $0$ and $2\\pi$ with respect to Bob's bases. This set of angles is going to be the input argument to our $CHSH$ circuit building function." ] }, { "cell_type": "code", "execution_count": null, "id": "6c1de1e7", "metadata": {}, "outputs": [], "source": [ "def make_chsh_circuit(theta_vec):\n", " \"\"\"Return a list of QuantumCircuits for use in a CHSH experiemnt\n", " (one for each value of theta in theta_vec)\n", " \n", " Args:\n", " theta_vec (list): list of values of angles between the bases of Alice and Bob\n", " \n", " Returns:\n", " List[QuantumCircuit]: CHSH QuantumCircuits for each value of theta\n", " \"\"\"\n", " chsh_circuits = []\n", " \n", " for theta in theta_vec:\n", " obs_vec = ['00', '01', '10', '11']\n", " for el in obs_vec:\n", " qc = QuantumCircuit(2,2)\n", " qc.h(0)\n", " qc.cx(0, 1)\n", " qc.ry(theta, 0)\n", " for a in range(2):\n", " if el[a] == '1':\n", " qc.h(a) \n", " qc.measure(range(2),range(2))\n", " chsh_circuits.append(qc)\n", "\n", " return chsh_circuits " ] }, { "cell_type": "markdown", "id": "190dbf81", "metadata": {}, "source": [ "Next, we are going to define a function for estimating the quantity $\\langle CHSH \\rangle$. One can define two of such quantities, actually, $\\langle CHSH1 \\rangle = \\langle AB \\rangle - \\langle Ab \\rangle + \\langle aB \\rangle + \\langle ab \\rangle$ and $\\langle CHSH2 \\rangle = \\langle AB \\rangle + \\langle Ab \\rangle - \\langle aB \\rangle + \\langle ab \\rangle$. Once chosen the corresponding measurement axes for both parties, each expectation value can be simply estimated by adding the counts from the output bitstrings with the appropriate sign (plus for the even terms $00$ and $11$ and minus for odd terms $01$ and $10$." ] }, { "cell_type": "code", "execution_count": null, "id": "c6e3e3be", "metadata": {}, "outputs": [], "source": [ "def compute_chsh_witness(counts):\n", " \"\"\"Computes expectation values for the CHSH inequality, for each\n", " angle (theta) between measurement axis.\n", "\n", " Args: counts (list[dict]): dict of counts for each experiment\n", " (4 per value of theta)\n", "\n", " Returns:\n", " Tuple(List, List): Tuple of lists with the two CHSH witnesses\n", " \"\"\"\n", " # Order is ZZ,ZX,XZ,XX\n", " \n", " CHSH1 = []\n", " CHSH2 = []\n", " # Divide the list of dictionaries in sets of 4\n", " for i in range(0, len(counts), 4): \n", " theta_dict = counts[i:i + 4]\n", " zz = theta_dict[0]\n", " zx = theta_dict[1]\n", " xz = theta_dict[2]\n", " xx = theta_dict[3]\n", "\n", " no_shots = sum(xx[y] for y in xx)\n", "\n", " chsh1 = 0\n", " chsh2 = 0\n", "\n", " for element in zz:\n", " parity = (-1)**(int(element[0])+int(element[1]))\n", " chsh1+= parity*zz[element]\n", " chsh2+= parity*zz[element]\n", "\n", " for element in zx:\n", " parity = (-1)**(int(element[0])+int(element[1]))\n", " chsh1+= parity*zx[element]\n", " chsh2-= parity*zx[element]\n", "\n", " for element in xz:\n", " parity = (-1)**(int(element[0])+int(element[1]))\n", " chsh1-= parity*xz[element]\n", " chsh2+= parity*xz[element]\n", "\n", " for element in xx:\n", " parity = (-1)**(int(element[0])+int(element[1]))\n", " chsh1+= parity*xx[element]\n", " chsh2+= parity*xx[element]\n", "\n", " CHSH1.append(chsh1/no_shots)\n", " CHSH2.append(chsh2/no_shots)\n", " \n", " return CHSH1, CHSH2" ] }, { "cell_type": "markdown", "id": "a217dc49", "metadata": {}, "source": [ "Finally, we are going to split the interval $[0, 2\\pi)$ into 15 angles and will build the corresponding set of $CHSH$ circuits." ] }, { "cell_type": "code", "execution_count": null, "id": "af544f5c", "metadata": {}, "outputs": [], "source": [ "number_of_thetas = 15\n", "theta_vec = np.linspace(0,2*np.pi,number_of_thetas)\n", "my_chsh_circuits = make_chsh_circuit(theta_vec)" ] }, { "cell_type": "markdown", "id": "c21b67b4", "metadata": {}, "source": [ "Now, let's have a brief look at how four of these circuits look like for a given $\\theta$." ] }, { "cell_type": "code", "execution_count": null, "id": "2ae3d3aa", "metadata": {}, "outputs": [], "source": [ "my_chsh_circuits[4].draw()" ] }, { "cell_type": "code", "execution_count": null, "id": "28fc7631", "metadata": {}, "outputs": [], "source": [ "my_chsh_circuits[5].draw()" ] }, { "cell_type": "code", "execution_count": null, "id": "e06c5583", "metadata": {}, "outputs": [], "source": [ "my_chsh_circuits[6].draw()" ] }, { "cell_type": "code", "execution_count": null, "id": "f11dd72c", "metadata": {}, "outputs": [], "source": [ "my_chsh_circuits[7].draw()" ] }, { "cell_type": "markdown", "id": "198541f1", "metadata": {}, "source": [ "These circuits are simply creating a Bell pair, and then measuring each party in a different basis. While Bob ($q_1$) always measures either in the computational basis or the $X$ basis, Alice's measurement basis rotates by the angle $\\theta$ with respect to Bob's." ] }, { "cell_type": "code", "execution_count": null, "id": "f9708e78", "metadata": { "scrolled": true, "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "# Execute and get counts\n", "result_ideal = sim.run(my_chsh_circuits).result()\n", "\n", "tic = time.time()\n", "transpiled_circuits = transpile(my_chsh_circuits, quito)\n", "job_real = quito.run(transpiled_circuits, shots=8192)\n", "job_monitor(job_real)\n", "result_real = job_real.result()\n", "toc = time.time()\n", "\n", "print(toc-tic)" ] }, { "cell_type": "code", "execution_count": null, "id": "28306b4d", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "CHSH1_ideal, CHSH2_ideal = compute_chsh_witness(result_ideal.get_counts())\n", "CHSH1_real, CHSH2_real = compute_chsh_witness(result_real.get_counts())" ] }, { "cell_type": "markdown", "id": "a71408d4", "metadata": {}, "source": [ "Now we plot the results." ] }, { "cell_type": "code", "execution_count": null, "id": "ad28a672", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "plt.figure(figsize=(12,8))\n", "plt.rcParams.update({'font.size': 22})\n", "plt.plot(theta_vec,CHSH1_ideal,'o-',label = 'CHSH1 Noiseless')\n", "plt.plot(theta_vec,CHSH2_ideal,'o-',label = 'CHSH2 Noiseless')\n", "\n", "plt.plot(theta_vec,CHSH1_real,'x-',label = 'CHSH1 Quito')\n", "plt.plot(theta_vec,CHSH2_real,'x-',label = 'CHSH2 Quito')\n", "\n", "plt.grid(which='major',axis='both')\n", "plt.rcParams.update({'font.size': 16})\n", "plt.legend()\n", "plt.axhline(y=2, color='r', linestyle='-')\n", "plt.axhline(y=-2, color='r', linestyle='-')\n", "plt.axhline(y=np.sqrt(2)*2, color='k', linestyle='-.')\n", "plt.axhline(y=-np.sqrt(2)*2, color='k', linestyle='-.')\n", "plt.xlabel('Theta')\n", "plt.ylabel('CHSH witness')" ] }, { "cell_type": "markdown", "id": "95416cc3", "metadata": {}, "source": [ "Note what happened! There are some particular combination of measurement bases for which $|CHSH| \\geq 2$. How is this possible? Let's look at our entangled bipartite system. It is easy to show that if $|\\psi \\rangle = 1/\\sqrt{2} (|00\\rangle + |11\\rangle)$, then the expectation value $\\langle AB \\rangle = \\langle \\psi|A \\otimes B| \\psi \\rangle = -\\cos \\theta_{AB}$ where $\\theta_{AB}$ is the angle between the measurement bases $A$ and $B$. Therefore, for the particular choice of bases $A = 1/\\sqrt{2}(\\sigma_z - \\sigma_x)$ and $a = 1/\\sqrt{2}(\\sigma_z + \\sigma_x)$, letting Bob measure with $B=\\sigma_z$ and $b=\\sigma_x$, we see that $|\\langle CHSH1 \\rangle| = 2\\sqrt{2} > 2$. It can also be shown that $2\\sqrt{2}$ is the maximum possible value attainable, even in the quantum case (dash-dotted line in the plot).\n", "\n", "The above inequality is called CHSH after Clauser, Horne, Shimony, and Holt, and it is the most popular way of presenting the original inequality from Bell.\n", "\n", "The fact that we violated the CHSH inequality in our real device is of significance. Just a decade ago such an experiment would have been of great impact. Nowadays, quantum devices have become significantly better and these results can be replicated easily in state-of-the-art hardware. However, there are a number of loopholes that have to be closed when violating the inequality in order to claim that either locality or realism have been disproven. These are the detection loophole (where our detector is faulty and fails to provide meaningful statistics) and the locality/causality loophole (where the two parts of the entangled system are separated by a distance smaller than the distance covered by the light in the time it takes to perform a measurement). Given we can generate entangled pairs with high fidelity and every measurement yields a result (this is, no measured particle is \"lost\"), we have closed the detection loophole in our experiments above. However, given the distance between our qubits (a few mm) and the time it takes to perform a measurement (order of $\\mu$s), we cannot claim we closed the causality loophole." ] }, { "cell_type": "markdown", "id": "892fdd27", "metadata": {}, "source": [ "### Send it after class\n", "\n", "Consider a game where Alice and Bob are put in separate rooms and each is given a bit $x$ and $y$, respectively. These bits are chosen at random and independently of each other. On receiving the bit each of them replies with a bit of their own, $a$ and $b$. Now, Alice and Bob win the game if $a$ and $b$ are different whenever $x=y=1$ and equal otherwise. It is easy to see that the best possible strategy for Alice and Bob is to always give $a=b=0$ (or $1$). With this strategy, Alice and Bob can win the game at most 75% of the time. \n", "\n", "Imagine Alice and Bob are allowed to share an entangled two-qubit state. Is there a strategy they can use that would give them a better chance of winning than 75%? (Remember that they can agree upon any strategy beforehand, but once they are given the random bits they cannot communicate anymore. They can take their respective parts of the entangled pair with them at all times, of course.)" ] }, { "cell_type": "code", "execution_count": null, "id": "96ee4803", "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [ "7d_uf8JI12oJ", "Li9fj6uVzyFR", "9PBnSGwum9ZJ", "s0UwnaaJQkqa", "YqAqumfLri_P", "yWcE6S_Qp61P", "yhGcFXBa4aEM", "ZocPglAL6zRm", "58JawO_lFBGY", "iTzbCQzm67Uw", "EQ8dJq6v7NW-" ], "name": "Workshop.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" }, "nbdime-conflicts": { "local_diff": [ { "diff": [ { "diff": [ { "key": 0, "op": "addrange", "valuelist": [ "3.9.4" ] }, { "key": 0, "length": 1, "op": "removerange" } ], 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