Richard Cleve

Introduction to Quantum Information Processing

C&O 681, CS 667, PHYS 767, C&O 481, CS 467, PHYS 667

Course Projects
Every student is required to submit a project by the last day of classes (which is worth 35% of the final grade). The project should be a written explanation of some topic in quantum information processing, selected with the approval of the instructor. A typical project is based on one or more research paper. A sample of research papers (from last year's course) is available here. Your paper should explain the topic in your own words, at a level accessible to your classmates.

You may work in teams of size two or three if you wish, with proportionately longer projects (10-20 pages per person for undergraduates and 15-25 pages for graduates).

Each project must be submitted in electronic format (PDF, PS, or Word).

Office Hours

By appointment or during the following times:

Richard Cleve Thursdays at 8:30-9:30am in DC 3524

Christoph Dankert Fridays Noon to 1:00pm in MC 5136A

Matthew McKague Thursdays Noon to 1:00pm in MC 6202

Colm Ryan Wednesdays 1:30 to 3:30pm in BFG (at the 2nd floor couch-and-whiteboard area in the IQC)

Assignments

Please submit assignments in the submission boxes on the third floor of the MC building (in box 3, slot 3, which should have my name on it)

Assignment 1 (PDF)
Assignment 2 (PDF)
Assignment 3 (PDF)

Objectives

Quantum Information Processing (QIP) seeks to exploit the quantum features of Nature to provide a qualitatively different and more powerful way of processing information than "classical" physics seems to allow. This course aims to give basic foundation in the field of quantum information processing (often just called "quantum computing"). QIP is a multidisciplinary subject and therefore this course will introduce fundamental concepts in theoretical computer science and physics that will enable students to pursue further study in various aspects of QIP.

Intended Audience

This course is intended for students majoring in CS, C&O or Physics, and is normally completed in a student's fourth year. It is intended to be accessible to students with either a CS/Math or Physics background with an interest in the physical and mathematical foundations of computation and/or the role of information in physics.

Prerequisites

A solid background in basic linear algebra (a strong performance in MATH 235 or Phys 364&365 should suffice) is necessary. Students will likely encounter at least one subject with which they have very little familiarity; this is expected. Familiarity with theoretical computer science or quantum mechanics will be an asset, though most students will not be familiar with both. The required background in both these areas will be presented in the course.

References

Quantum Computation and Quantum Information, by Nielsen and Chuang (Cambridge University Press)

Outline of Topics

General introduction to the quantum mechanical framework, including protocols for superdense coding and teleportation.

Simple quantum algorithms, including the algorithms of Deutsch, Deutsch-Jozsa, and Simon.

Computational frameworks, including classical and quantum models of computation, simulations between them, and basic complexity classes.

Shor's factoring algorithm, including the quantum Fourier transform, and order-finding.

Grover's search algorithm, including amplitude amplification, and applications to combinatorial search problems.

Quantum error correction, including Shor's 9-qubit code and Calderbank-Shor-Steane (CSS) codes.

Physical realizations of quantum information processing devices.

Introduction to quantum cryptography, including the Bennett-Brassard (BB84) scheme and the bit commitment problem.

Nonlocal operations and communication complexity.

Evaluation

3 assignments (15% each)

1 mid-term exam (20%)

1 project (35%)