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. |
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. |
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 |
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. |
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]. |
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. |
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. |
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. |
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: |
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. |
|
Appendix A |
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. |
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. |