Lecture Dates Book Sections Comments
05-04, 05-06 13.5 The last week of classes ends with an analysis of Shor's quantum solution to the Discrete Logarithm Problem.

Videos: 05-04 and 05-06.

04-27, 04-29 13.4, 13.5, 13.3 This week, we complete our discussion of the Eigenvalue Approximation algorithm before turning to further analysis of Shor's factoring algorithm.

Videos: 04-27 and 04-29.

04-20, 04-22 13.2, 13.5 We complete our discussion of the solution to the HSP for general (finite) Abelian groups before moving on the Shor's algorithm. In preparation for Shor's algorithm, we will cover the Quantum Fourier Transform (QFT) and the Eigenvalue Approximation (section 13.5) algorithms

Videos: 04-20 and 04-22.

04-13, 04-15 13.1 We will complete our discussion of Simon's problem this week before examining the hidden subgroup problem for general finite Abelian Groups. I have written some self-contained notes about this proof, so please consult them in addition to lecture.

Notes on the Abelian HSP: [pdf] [tex].

Videos: 04-13 and 04-15.

04-06, 04-08 10.1, 10.2, 13.1, Group Theory Historically, Simon's problem was the second problem to exhibit superpolynomial speedup on a quantum computer. It is a special case of the Hidden Subgroup Problem, which is an area of active research.

If you're unfamiliar with cosets in group theory, you should read the MIT opencourseware notes on them [pdf].

Videos: 04-06 and 04-08.

03-30, 04-01 None We will be covering the material from sections 1-4 of the paper Quatum lower bounds by quantum arguments by Ambainis. The paper assumes quite a bit of previous knowledge, but the lecture will be as self-contained as possible.

Videos: 03-30 and 04-01.

03-23, 03-25 8.2, 9.1, 9.2 This week, we will be covering our first quantum algorithm, Grover's algorithm in some detail.

Videos: 03-23 and 03-25.

03-16, 03-18 8.1, 8.2 Please remember that our midterm exam is scheduled for 03-18 this week.

Videos: 03-16

03-09, 03-11 6.3, Chapter 7 Chapter 7 connects classical computation to quantum computation in a very careful analysis. You should carefully read this chapter in order to fully understand the exact relationship between these two models of computation.

Videos: 03-09 and 03-11.

03-02, 03-04 Part 2 (53-54), 6.1, 6.2 This week, we begin the second third of the course where we discuss the computational model for quantum computation. The language of quantum mechanics is complex coordinate-free linear algebra, which the book assumes some familiarity with. You should read the section in the book, and also consult the following two resources for additional details:

Videos: 03-02 and 03-04.

02-23, 02-25 Appendix A, 4.2, 4.3 We finish our discussion of number theory and bring it to bear on proving the correctness of the Miller-Rabin algorithm.

Videos: 02-23 and 02-25.

02-16, 02-18 Appendix A, 4.2 We embark this week on a quick survey of the basic number theory required to understand the Miller-Rabin algorithm and Shor's quantum factoring algorithm. Please read Appendix A carefully and consult online resources (or ask during office hours) if there are any topics you struggle with.

Videos: 02-18.

02-09, 02-11 Chapter 3, 4.1 We continue our discussion of complexity theory, covering NP, Karp reducibility, and the classes NP-hard and NP-complete. Finally, we turn our attention to the complexity class BPP and start building some of the machinery for the Miller-Rabin primality algorithm.

Definition 4.1 on p36 is incorrect. The last part of it should read "M gives answer 'no' with probability >= 1-e" (similar to the line above). The point is that the probability of error is at most e.

Videos: 02-09 and 02-11.

02-02, 02-04 Chapter 1, 3.1 Read this chapter carefully. This material should be review from your foundations of computation course, EECS 510, so pay special attention to any unfamiliar parts.

Videos: 02-04.