Syllabus¶
Course Title |
PHYS437 PRACTICAL QUANTUM COMPUTING FOR SCIENTISTS |
---|---|
Lecturers |
Barış Malcıoğlu |
Grading |
Midterm %20, Term project %40, Hands-on sessions & homeworks %40 |
Tentative Course Contents¶
Chapter 1: Review & Mathematical Foundation¶
Linear Algebra
- Review of the four postulates of quantum mechanics
Postulate 1: Individual quantum systems
Postulate 2: Quantum operations
Postulate 3: Composite quantum systems
Postulate 4: Measurement
No cloning theorem
Quantum entanglement
- Density matrices
The partial trace operation
Using partial trace to detect entanglement
How the postulates of quantum mechanics apply to density operators
Chapter 2: Quantum Circuit Diagrams¶
Quantum Circuit Diagrams
- Quantum operators
Unary
Binary
Ternary
Comparison with classical gates
The universality of Quantum operators
The Bloch Sphere
Chapter 3: Complexity Theory; Entropy and Entanglement Distillation¶
- Complexity Theory
Time Complexity
Complexity Classes
- Entropy
Shannon entropy
Von Neumann Entropy
Quantifying entanglement in composite quantum systems
Entanglement distillation
Chapter 4: The Deutsch-Josza and Berstein-Vazirani algorithms¶
Functions as oracles
The problem: Is f constant or balanced?
- The algorithm
A naive idea
Deutsch’s algorithm
The phase kickback trick
The Deutsch-Josza algorithm
The Berstein-Vazirani algorithm
Chapter 5: Strategies of Input Encoding¶
Basis Encoding
Amplitude Encoding
Time-Evolution Encoding
Hamiltonian Encoding
Chapter 6: Simon’s algorithm and applications to cryptography¶
- Simon’s algorithm
Birthdays and a naive classical algorithm
Simon’s algorithm
Application to cryptography
Chapter 7: The Quantum Fourier Transform¶
From Vandermonde matrices to the Discrete Fourier Transform
The Quantum Fourier Transform (QFT)
Quantum Phase Estimation (QPE)
Applications of QPE
Quantum algorithms for QPE
Chapter 8: Shor’s quantum factoring algorithm¶
The integer factorization problem
- The factoring algorithm
Reducing FACTOR to order-finding
Sampling via QPE
Postprocessing via continued fractions
Application: Breaking RSA
Chapter 9: Variational Circuits as Machine Learning Models (time permitting)¶
- How to Interpret a Quantum Circuit as a Model
Deterministic Quantum Models
Probabilistic Quantum Models
An Example: Variational Quantum Classifier
An Example: Variational Generator
- Which Functions Do Variational Quantum Models Express?
Quantum Models as Linear Combinations of Periodic Functions
An Example: The Pauli-Rotation Encoding
- Training Variational Quantum Models
Gradients of Quantum Computations
Parameter-Shift Rules
Barren Plateaus
Generative Training
- Quantum Circuits and Neural Networks
Emulating Nonlinear Activations
Variational Circuits as Deep Linear Neural Networks
Time-Evolution Encoding as an Exponential Activation
Hands-On sessions¶
There will be homework for lab sessions.
Attendance to all of the hands-on sessions, and submitting the assigned hands-on work is mandatory. Any missed hands-on session, or assigned hands-on work will result in N/A grade. Only officially documented cases (such as medical reports) will be considered for exemption.
Midterm¶
The midterm exam will involve a theory part and a programming part.
The theory part should be answered using a Latex/Word processor, converted to pdf.
The programming part must be an ASCII text file containing python code (*.py).
- red:
The files should be uploaded to supplied Turnitin interface. Any incompatible input will be disregarded.
Term projects¶
Participants are expected to present a project involving Quantum Computation, Quantum Communication, or Quantum hardware.
The term project is the final exam.
There are two parts: Presentation (~20 minutes), Q&A session after the talk (~10 minutes)
The presenter will be graded according to the scientific quality of the presentation
The audience will be graded according to their participation in the Q&A session.
The term projects will be presented in the last 3-4 weeks
Attendance to the term project presentations is mandatory. The first missed week will result in a reduction of your final grade to %65. The second missed week will result in a reduction of your final grade to %35. If you miss three weeks, you will receive N/A grade.
Only one missed week might be allowed with a valid official excuse.
Textbooks¶
Theory Content:¶
“Quantum Computing for the Quantum Curious” Ciaran Hughes, Joshua Isaacson, Anastasia Perry, Ranbel F. Sun, Jessica Turner https://doi.org/10.1007/978-3-030-61601-4 (open Access)
“Quantum Computing: Lecture Notes” Ronald de Wolf arXiv:1907.09415
“Introduction to Quantum Computation” Sevag Gharibian (Can be obtained from his course page here)
Lab Content:¶
“Quantum Computing: An Applied Approach” Jack D. Hidary https://doi.org/10.1007/978-3-030-23922-0
Optional content (time permitting):¶
“Lectures on Quantum Tensor Networks” Jacob Biamonte (for a systematic connection between circuit diagrams and CV systems)
“Machine Learning with Quantum Computers” Maria Schuld, Francesco Petruccione https://doi.org/10.1007/978-3-030-83098-4