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Quantum Computation

Arizona State University, Fall 2023

When: Tuesdays and Thursdays noon–1:15pm

Where: COOR 184

Instructor: Zilin Jiang ([email protected])

Office hours: Tuesdays and Thursdays 1:30pm–2:30pm at WXLR A839

Teaching assistant: Vinayak Sharma ([email protected])

Course description​

In this guided tour, we will explore quantum computation from the perspective of theoretical computer science. Topics include quantum algorithms, quantum error correction, and quantum information.

Prerequisites: A strong undergraduate background in linear algebra, discrete probability, and theory of computation. No background in physics is required.

Required textbook: Mermin, N. David. Quantum computer science: an introduction. Cambridge University Press, 2007. library

Onboarding:

Asking questions: For class-related questions it is best to come to office hours.

Grading​

Homework 60% + Midterm 15% + Final 25% + Bonus 10%

No make-up test will be given unless a student has notified the instructor before the test is given.

  • Midterm: noon–1:15pm, October 19, 2023. COOR 184
  • Final: noon–2pm, December 5, 2023. COOR 184

Homework​

All steps should be justified. You are strongly encouraged to do as much homework as possible individually; you will gain the most out of the course this way.

Sources and collaboration policy. Collaboration and use of external sources are permitted, but must be fully acknowledged and cited. Collaboration may involve only discussion; all the writing must be done individually. Failure to do so will be treated as cheating (see What is Academic Integrity?).

Late policy. In general no late homework will be accepted unless there is a genuine emergency backed up by official documents.

  1. Homework 1 (due on August 31)
  2. Homework 2 (due on September 19)
  3. Homework 3 (due on October 5)
  4. Homework 4 (due on October 26)
  5. Homework 5 (due on November 14)
  6. Homework 6 (due on November 27)

Schedule​

Week 1

  • August 17: Introduction to the class structure and brief on computational complexity

Week 2

  • August 22: Introduction to probabilistic classical computation, Freivalds' matrix multiplication checker and primality testing
  • August 24: Introduction to the Qbit, basic quantum computation ideas and Dirac Bra-Ket notation.

Week 3

  • August 29: Introduction to other basis state, Measuring in {|+⟩, |-⟩} basis, Polarized lens experiments, EV Bomb Test
  • August 31: Increasing probability for EV Bomb Test, Intro to single qubit transformations, X-Gate, Hadamard Gates, Quantum Gate Properties → Unitary Matrices and their properties, S-gate and Z-Gate (Phase Shift), Multi dimension transforms → Swap Gate

Week 4

  • September 5: Unitary Matrix properties and examples, Rotational formulation of EV bomb, Discriminating States, Error in discriminating non orthogonal states, Intro to multi-qubit systems, Tensor Product Representation
  • September 7: CNOT Gate, EPR Pairs, Proving entanglement through CNOT, Computation on entangled states, Measurement on 2 qubit systems, Partial Measurement, Mixed State

Week 5

  • September 12: CHSH game
  • September 14: Bell's Inequality, Quantum Teleportation

Week 6

  • September 19: No cloning theorem, Niesners Scheme, Non-Counterfeitability, Upshot
  • September 21: Quantum Money, Wiesner's Scheme, Public Key Quantum Money, Policy Discussion

Week 7

  • September 26: Simulating probabilistic classical computations with a quantum computer (ancilla bits, reversibility)
  • September 28: Uncomputing Garbage values.

Week 8

  • October 3: Boolean Fourier Transform, Bernstein-Vazirani Algorithm
  • October 5: Deutsch-Jozsa Algorithm

Week 9

  • October 10: No class (Fall break)
  • October 12: Simon's Algorithm

Week 10

  • October 17: Quantum Fourier Transform (QFT)
  • October 19: Midterm.

Week 11

  • October 24: Discrete Fourier Transform and L-Periodic functions
  • October 26: Approximate Period finding algorithm, Period finding to Factoring

Week 12

  • October 31: Intro to Group Theory
  • November 2: Group Theory: Sub-Groups, Hidden Sub-Group Problem, Shor's Algorithm, Grover's Algorithm

Week 13

  • November 7: Grover's Algorithm (continued)
  • November 9: Adversarial Methods

Week 14

  • November 14: Adversarial Methods with Hamming distance, Density Matrices
  • November 16: Mixed States

Week 15

  • November 21: Quantum Probability Theory
  • November 23: No class (Thanksgiving)

Week 16 — Student Presentation Week

  • November 28: Student Presentation 1
  • November 30: Student Presentation 2
  • December 5: Final exam