Introduction to Quantum Information Processing
QIC 710, CS 768, CO 681, PHYS 767, AMATH 871, PMATH 871 (Fall 2022)

Instructor: Richard Cleve (
Note to
students: please include QIC-710 in email subject, regardless of the version you’re in

Connor Paul-Paddock ( office hour*: Wednesdays, 4-5pm (on Zoom)
Vahid R. Asadi ( office hour*: Mondays, 11am-Noon (in QNC 3117)
Yuming Zhao ( office hour*: Wednesdays, 3-4pm (in QNC 4203)
* if there are any changes, they will be noted here

Course web site:

Classes: Tuesdays and Thursdays 4:00-5:20pm in MC 4040 and sometimes in QNC 0101:
      • Tuesday, November 22: QNC 0101
      • Thursday, November 24: QNC 0101

General course information [here]

Lecture videos [here]

Lecture notes [here]


  • Schedule of presentations is here (last updated on Nov. 22)
  • 11/21 Assignment 5 has been posted (due December 6).
  • 11/8 The due date for Assignment 4 is extended until Monday, November 14 (11:59pm).
  • 10/3 Assignment 4 has been posted (due November 10).
  • 10/25 Some people who studied the proof of the classical lower bound for Simon's problem in the lecture notes (Quantum Algorithms, Part 1) pointed out that some parts of the proof were not clear. I agree. I revised the paragraph surrounding Eq. (14) on page 35. I hope the revised version is clearer. Also I implemented the errata that I received from people in the class — thanks so much for that!
  • 10/24 The due date for Assignment 3 is extended until Monday, October 31 (11:59pm).
  • 10/21 There is an error in question 2(c) of Assignment 3. It has been updated with a correction.
  • 09/23 Assignment 3 has been posted (due October 27).
  • Note: the terminology for modular arithmetic occurs in these two forms:
    1. An equivalence relation:
    ab (mod m) means m divides a – b.
    2. A binary operation:
    a mod m is the unique b{0, 1, ..., m – 1} such that ab (mod m).
  • 10/11 Some references for the basics of modular arithmetic and definitions of rings and fields:
    - Modular arithmetic (AoPS) [here]
    - An Introduction to Groups, Rings, and Fields (H.A. Priestley) [pdf]
  • 10/04 The due date for Assignment 2 has been extended to Tuesday, October 11.
  • 09/29 In the last class, a very simple "quantum secret sharing scheme" came up (as something complimentary to the no-cloning theorem) and this resulted in inquiries about the details of more general secret sharing schemes. If you're interested, more information is [here].
  • 09/23 Assignment 2 has been posted (due October 6).
  • Office hours have been posted; see above (these are for this week and might change in future weeks).
  • 09/16 For Assignment 1: you may assume the following fact without proof: If, for vectors v_0, v_1, w_0, w_1 in a d-dimensional space it holds that the inner product between v_0 and v_1 is the same as the inner product between w_0 and w_1, then there exists a d x d unitary U such Uv_0 = w_0 and Uv_1 = w_1.
  • 09/12 An error in Assignment 1 has been corrected in question 2(a). Please see the current version.
  • Assignment 1 has been posted (due September 22).
  • Error: in class I incorrectly claimed that bit 0 vs. a uniformly random bit can be distinguished with worst-case success probability ¾. In fact, ⅔ is the best possible, by the method described by a student.
  • First class is on September 8.

Assignments (60% of grade)

Assignment 1 (due September 22)
Assignment 2 (due October 6, extended to October 11)
Assignment 3 (due October 27, correction to Q2(c), extended until October 31, 11:59pm)
Assignment 4 (due November 10, extended until Monday, November 14)
Assignment 5 (due December 6)

Projects (40% of grade)
Each project is an oral presentation to the class. It should explain and analyze some topic in quantum information processing, selected with the approval of the instructor. Your presentation should be about 25 minutes in length. You should explain the topic in your own words, at a level accessible to your classmates. More information about the project component is [