CS571, Introduction to Quantum Computation

Prerequisites

To take this course you need to be confident in 1) and 2) below, and have some understanding of 3). In the CS department some of these things are taught in CS530; if you took that course you should have done well in it if you want to take this one.

1. Linear algebra: what are the eigenvectors and eigenvalues of a matrix? What is its inverse and transpose? What is the inner product between two vectors? What is an orthonormal basis? What does it mean to diagonalize a matrix by changing basis? Why do we change basis (transform) a matrix by conjugating it by another? What does it mean to project a vector into a subspace?

2. Complex numbers: what is the complex conjugate of a complex number? What it its phase? What is its magnitude? What is e^(i theta)?

3. Fourier analysis: what is the Fourier transform? Why do the basis functions e^(i omega x) form an orthonormal basis? The Fourier transform is a linear transformation; what matrix carries it out? What is its inverse? Why does the Fourier transform change convolution into multiplication and vice versa?

Books and notes

There are three books that are recommended: none are required. These are Nielsen and Chuang, Quantum Computation and Quantum Information; Kaye, Laflamme, and Mosca, An Introduction to Quantum Computing; and Moore and Mertens, The Nature of Computation. You can get this last one at a discount through my web page.

Lectures will be self-contained: please take good notes.

Grading

Grades will be based on several problem sets. Collaboration is allowed, and even encouraged; direct copying is not.

Office hours

My office is in Farris Engineering Center, FEC335. My office hours are Tuesdays after class, on Tuesdays from 2:00 to 3:00 p.m., or by appointment. You should also feel free to email me, which is often the quickest way to get help.

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