Syllabus

Course 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:

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