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This is an introductory course on quantum computation and quantum information.
I assume a basic knowledge of linear algebra and probability. We will cover most of the chapters in
the textbook by Kaye, Laflamme and Mosca (KLM) with a few additional topics on quantum information theory taken from the
book by Nielsen and Chuang (NC). A few more topics
will be covered if there is time.

Textbook: An Introduction to Quantum Computing by P. Kaye, R. Laflamme, and M. Mosca. (Oxford University Press)

I will be covering most of the topics in this text. A few additional topics on quantum information theory will be taken from Nielsen and Chuang.

Course topics. Detailed outline.

- Introduction
- Linear algebra
- Quantum mechanics
- Circuit model of quantum computation
- Simple quantum protocols
- Simple quantum algorithms
- Efficient quantum algorithms
- Quantum complexity theory
- Quantum information theory
- Quantum error correction
- Additional topics(time permitting)

Grading policy (Tentative)

35% mini-quizzes and homeworks, 35% project+presentation, 30% Finals.

News and announcements

Class will be shifted to ESB 350 from 01/08/2013.

Lectures

- 29 Jul Introduction

- 01 Aug Linear algebra review

- 02 Aug Linear algebra review

- 19 Aug Quantum mechanics--State space and evolution postulates

- 22 Aug Quantum mechanics--Composite systems and measurement postulates

- 23 Aug Quantum mechanics--Measurement postulate and reformulation using density matrices

- 26 Aug Circuit model of quantum computation and Superdense coding

- 29 Aug Quantum teleportation

- 30 Aug Arbitrary single qubit gates and 2 qubit controlled gates, Miniquiz-1

- 02 Sep Universal sets of quantum gates (2 lectures)

- 05 Sep Measurements and the circuit model, Quantum key distribution

- 06 Sep Deutsch, Deutsch-Jozsa algorithms, Miniquiz-2

- 12 Sep Deutsch-Jozsa, Bernstein Vazirani algorithms

- 13 Sep Simon's problem

- 16 Sep Phase estimation problem (exact), Miniquiz-3

- 19 Sep Phase estimation problem (approximate), Quantum Fourier transform

- 20 Sep Applications of phase estimation algorithm, order finding

- 23 Sep Order finding (continued), Miniquiz-4

- 26 Sep Factoring

- 27 Sep Discrete log and Hidden subgroup problem

- 30 Sep Grover's quantum search algorithm

- 03 Oct Amplitude amplification

- 04 Oct Quantum complexity theory, Miniquiz-5

- 07 Oct Quantum complexity theory (continued)

- 11 Oct Quantum error correction (bit flip code)

- 14 Oct Shor's nine qubit code

- 17 Oct Steane's code

- 21 Oct Classical codes to Steane's code

- 24 Oct CSS codes

- 25 Oct Quantum fault tolerance and threshold theorem

- 28 Oct Classical information theory, basic concepts

- 01 Nov Quantum information theory, basic concepts

- 04 Nov Schumacher's noiseless coding theorem

- 07 Nov Wrapup