Math 410/510: Introduction to Quantum Computing, Spring 2021

Instructor: Chi-Kwong Li

Meeting time and format:
• For Math410-01, TR 9:30 - 10:50 a.m. via Zoom (address will be posted on blackboard).
• For Math410-03, watch Zoom videos (links will be posted on blackboard).
  
Office: Jones 128, Tel: 221-2042
E-mail: ckli@math.wm.edu, http://cklixx.people.wm.edu
Office hours: Wednesday 2:00 - 3:00 via zoom (same zoom address for lectures), or by appointment.

• M. Nakahara and T. Ohmi, Quantum computing: From Linear Algebra to Physical Realizations,
  CRC Press, Taylor and Francis Group, New York, 2008.
  http://www.amazon.com/Quantum-Computing-Algebra-Physical-Realizations/dp/0750309830

Additional references:

• Nielsen and Chuang, Quantum Computation and Quantum Information Science, Cambridge.
• Watrous, The Theory of Quantum Information, Cambridge.
• Yanofsky and Mannucci, Quantum Computing for Computer Scientists, Cambridge.
• The Functional Analysis of Quantum Information Theory a collection of notes based on lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter. https://arxiv.org/pdf/1410.7188.pdf

Homework

• There will be 12 homework sets. Pdf files of the solutions should be uploaded to the blackboard by the due dates.
• Challenging problems will be assigned from time to time, extra-credits will be given to successful (or partially successful) attempts.
• Homework help will be provided during office hours.
• Math 510-01 students are required to write term papers.
• You have to use LaTex to typset mathematical document, an excellent skill to acquire. You may get the programs for free.
  • For windows users,
    (a) download the MikTex program from http://miktex.org/download;
    (b) then download the Texmaker program from http://www.xm1math.net/texmaker/download.html;
    (c) then open the program "texmaker";
    (d) copy (or download and then open) the "homework01.tex" file to the texmaker window;
    (e) select "LaTex" from the "Quick Build" menu;
    (f) click the "=>" arrow on the left of "Quick Build" to get the pdf output.
    
  • For Mac users,
    (a) download MacTex from http://tug.org/mactex/;
    (b) open the "texshop" program,
    (c) copy (or download and then open) the "homework01.tex" file to the texshop window;
    (d) change "PlainTex" to "LaTex" at "Typeset" menu;
    (e) click "Typeset" icon to get the pdf output.
    
  • You may also use the online editor Write LaTeX .
  • Here is a list of TeX commands for mathematics symbols.

Prepare your solution in LaTex, and upload the pdf file of your solution.
Sample LaTex file for typsetting. [ Tex file | pdf file ]

• Homework 1. Due: Feb. 10. Exercise 1.1 - 1.7, 1.9, 1.11, 1.12. Extra Crdit. 1.8, 1.10. [ Sample solution.]
  Scan of the questions from the book. [ file-1 | file-2 | file-3 ]
• Homework 2. Due: Feb. 17. Exercises 1.13 - 1.17, 1.20 - 1.22. [ Sample solution.]
  [ file-1 | file-2 ]
• Homework 3. Due: Feb. 24. [ Sample solution.]
  Exercises 2.2-2.7 [ file-1 | file-2 |
• Homework 4. Due: March 3. Exercises 2.8-2.11. Exercises 3.1-3.5. [ Sample solution.]
  [ file-1 | file-2 | file-3 ]
• Homework 5. Due: March 12. Exercises 2.8-2.11. Exercises 3.6, 4.1-4.7. [Hint.]
  [ Sample solution.]
  
• Homework 6. Due: March 19. Exercise 4.8 - 4.17.[You may use pencil paper to draw the circuit diagrams. To show that two diagrams produce the same unitary operators, just check the actions on $|0000\ra, ...., |1111\ra$.]
  [Hint.| Homework session note.] [ Sample solution.]
  
• Homework 7. Due: March 28, Exercises 5.1-5.2. Exercises 6.1-6.4. Hint.] [ Sample solution.]
  
• Homework 8. Due: April 7, Exercises 6.5 - 6.8. Exercises 7.1-7.3. Extra credit. 7.4. [ Sample solution.]
  
  
• Homework 9. Due: April 18, Exercises 8.1-8.4. [ Note.| [ Sample solution.]
  
• Homework 10. Due: April 25. Exercises 9.1, 9.2. [ Sample solution.]
  Question 3. For each of the followingone quibt channel, construct the Choi matrix and show that it is positive semidefinite.
  
  (a) Bit-Flip Channel,
  (b) Phase-Flip Channel,
  (c) Depolarizing Channel.
  (d) Amplitude-Damping Channel.
  
  Question 4. Consider the linear map T: M_2 -> M_2 defined by T(A) = A^t (the transpose of A).
  
  (a) Show that T is linear.
  (b) Show that if A in M_2 is a density matrix, then so is T(A).
  (c) Show that T is not a quantum operation by showing that its Choi matrix is not positive semidefinite.
  
  Optional (extra credit). Exercise 9.3.
• Homework 11. Due: May 2. Exercises 10.1-10.7.
• Homework 12. Due: May 17. Exercises 10.8-10.11.
  [ Sample solution.]

                Homework    Final   Presentation/Paper

     Math 410          60%        40%
     Math 510          55%        35%         10%

          (Extra credit problems may add up to  another 5%)

     Final      May. 17    3    hrs   (9:00-12:00)

     Grades (for homework, exams, final grade, etc.):

     %: 0 - 60 - 65 - 70 - 75 - 80 - 83 - 87 - 90 - 93 - 100
          F    D    C-   C    C+   B-   B    B+   A-    A