CS 264, Fall 2009

CS 264
Quantum Computation
Fall 2009

Instructor

Sandy Irani
4042 Bren Hall
irani@ics.uci.edu

Class Times and Place

T-Th 11:00AM-12:30PM
Bren Hall 1423
No class: Oct 15, 22, 27
Extra lecture: Tue, Dec 8, 10:30-12:30pm

Course Overview

This course will provide an introduction to the field of quantum computation with an emphasis on computational complexity. Below is a list of some of the topics that will be covered:

Introduction to quantum mechanics from the perspective of quantum information.
Formal models of quantum computation and quantum complexity classes.
Quantum algorithms: quantum fourier transform and applications (including Shor's algorithm for factoring), quantum search, quantum simulation.
Limitations on quantum computation: lower bounds for search, the class QMA and hardness results for computing fundamental properties of quantum systems.
Quantum entanglement, especially as it pertains to computational complexity.

Depending on time, I may give a couple overview lectures on important areas in quantum computation which we will not have time to cover in detail. Topics will hopefully include error correction and fault-tolerant computation as well as quantum cryptography.

Prerequisites

No formal course requirements. Students with a strong background in either computer science, mathematics, physics or chemstry are welcome to attend.

Course Requirements

Problem sets will be given every two weeks. Students are also expected to provide typed and formatted scribe notes for two or three lectures which will be posted on the course web page. Students may elect to do a project in lieu of the last problem set. This could be a paper (original work or survey paper) or a presentation in class.

Reading list

There is no required text for the course. The following is a list of books and course notes that may be useful. At the beginning of each lecture, I will point to recommended references for the material to be presented.

Kitaev, Shen and Vyalyi, Classical and Quantum Computation
Nielsen and Chuang, Quantum Computation and Quantum Information
Mermin, Quantum Computer Science
Umesh Vazirani's Course Notes on Quantum Computation: link.
John Preskill's Course Notes on Quantum Computation: link
Scott Aaronson's Course Notes on Quantum Complexity Theory: link
Scott Aaronson's Course Notes on Quantum Computing Since Democritus: link
Qubits, Quantum Mechanics and Computers: Course Notes link .
Andrew Child's course on Quantum Algorithms: link .

Lecture Topics

Date	Topic
Sep 24	Quantum Mechanics Postulates, Qubits
Sep 29	Observables, Hamiltonian, Schrodinger's Eqn
Oct 1	Tensor products, Entanglement, Bell Inequalities
Oct 6	Quantum circuits, Universal gate sets
Oct 8	Quantum Complexity Classes, QFT over Z_2^N Deutsch-Jozsa
Oct 13	BQP in PSPACE, Simon's Algorithm
Oct 20	QFT over Z_N, Factoring reduces to Order Finding
Oct 29	Shor's Factoring Algorithm
Nov 3	Factoring Recap, Hidden Subgroup Problem
Nov 5	Phase Estimation, Discrete Log
Nov 10	Lower Bound for Unstructured Search
Nov 12	Grover Search, Quantum Simulation
Nov 17	Search by Quantum Walk
Nov 19	Quantum Hitting Time
Nov 24	Quantum Walk Algorithm for Search and Element Distinctness
Dec 1	Adiabatic Quantum Computation
Dec 3	QMA-completeness
Dec 8	Error Correcting Codes

CS 264 Quantum Computation Fall 2009