(Spring Term 2014)

Department of Physics and Astronomy, University of Pittsburgh

This course is offered by the Physics Department of Carnegie-Mellon University, with assistance from the Computer Science Department and the Department of Physics and Astronomy of the University of Pittsburgh. The level is appropriate for advanced undergraduates and beginning graduate students.

The course comes in two versions: a 10 unit course 33-658 and a 12 unit course 33-758. The lectures, problem assignments, examinations, and term paper are the same for both. The 12 unit course involves additional work as indicated below under COURSE REQUIREMENTS.

33-658 or 33-758COURSE NUMBER:

10 for 33-658, 12 for 33-758UNITS:

Tuesday, Thursday, 3:00 PM to 4:15 PMHOURS:Seminar for 33-758 will be Tuesday or Thursday, 4:30 to 5:30 PM

Wean Hall 7316CLASSROOM:

Tuesday, Jan. 14, 2014FIRST CLASS MEETING:

INSTRUCTORS:Robert Griffiths, Physics Department, Carnegie-Mellon

Telephone: 268-2765

Email: rgrif AT cmu.eduDaniel Stahlke, Physics Department, Carnegie-Mellon

Email: dstahlke AT andrew.cmu.edu

CONSULTANT:Prof. Avrim Blum, Computer Science Department, Carnegie-Mellon

Telephone: 268-6452

Email: avrim AT cs.cmu.edu

COURSE SYLLABUS:

The following list is subject to change.

I. Introduction to quantum mechanics

- Hilbert space
- Unitary and stochastic dynamics
- Probabilities and measurements
- Entanglement
- Density operators and correlations
II. Introduction to quantum information

III. Quantum algorithms

- Classical information theory
- Quantum information types and quantum channels
- Dense coding
- Teleportation
- No cloning
- Quantum cryptography
IV. Physical realizations

- Classical computation
- Shor factorization
- Grover search
- Measurement-based computation
V. Noise and error correction

- Optical lattices

- Quantum operations
- Graph states and codes
- Quantum error correction
- Fault-tolerant computation

COURSE REQUIREMENTS:Problems will be assigned weekly, and should be turned in on time if you expect them to be graded.

You are welcome to discuss problems with anyone. However, the assignment is then to be written up separately by each individual. This includes writing your own computer program (for plotting, or whatever) when that is required. Copying what others have written and turning it in as your own work is a violation of university policy on cheating and plagiarism.

There will be two in-class exams during the term. In place of a final exam, you are to prepare a term paper, on the order of 15 to 20 pages, to turn in at the end of the course. The topic should have something to do with quantum computation or information theory, and must be approved by the instructor. It is always best to choose something you find interesting or exciting. A one page proposal will be due at a time to be announced later.

For the

twelve unit course, 33-758, you are expected to attend a weekly seminar, make a few comments about it on the next problem assignment, and give a short talk yourself at some point during the semester, or else something equivalent; e.g., write a brief report on a published paper.

PREREQUISITES:Students should be familiar with linear algebra of complex vector spaces, or prepared to rapidly learn it on their own. Chapter 3 of Griffiths,

Consistent Quantum Theory, contains the essentials.Quantum theory is not a prerequisite, and appropriate quantum concepts will be introduced as needed. Some prior knowledge will prove helpful, and 33-234 or 33-445 (33-755) are recommended.

Algorithms and complexity theory are not prerequisites, and the appropriate concepts will be introduced as needed. Some prior knowledge of these topics, as treated in 15-211, 15-251, or 15-451, will prove helpful.

Assignments

- Assignment 1, due Jan. 21
- Assignment 2, due Jan. 28
- Assignment 3, due Feb. 4
- Assignment 4, due Feb. 11
- Assignment 5 , preparation for hour exam on Feb. 18
- Assignment 6, due Feb. 25
- Assignment 7, due Mar. 4
- Assignment 8, due Mar. 18
- Assignment 9, due Mar. 25
- Assignment 10, preparation for hour exam on April 1
- Assignment 11, due April 8
- Assignment 12, due April 15
- Assignment 13, due April 22
- Assignment 14, due April 29

Course Notes

- Hilbert Space Quantum Mechanics
- Unitary Dynamics and Quantum Circuits
- Probabilities
- Stochastic Quantum Dynamics I. Born Rule
- Histories and Consistency
- Measurements
- Density Operators and Ensembles
- Classical Information Theory
- Quantum Information Types
- Types of Quantum Information (Phys. Rev. A 76 (2007) 062320, arXiv:0707.3752 [quant-ph])
- Dense Coding, Teleportation, No Cloning
- Quantum Channels, Kraus Operators, POVMs

- Quantum Error Correction

- Graph States and Graph Codes

- Measurement-Based Quantum Computation

Lectures

- Classical Algorithms, Avrim Blum, February 13 and 20, 2014
- Physical implementations of quantum computing I, Physical implementations II, Andrew Daley, April 3 and 8, 2014

Quantum Information Seminar

- Toy Model of Time-Delay Interference, Robert Griffiths, March 18, 2014

Text Book

The text book for the course will be

Quantum Computation and Quantum Informationby M. A. Nielsen and I. L. Chuang (Cambridge, 2000).In addition the book

Consistent Quantum Theoryby R. B. Griffiths (Cambridge 2002) is recommended for part I of the course. Copies will be kept on reserve in the library. The book is available online here.

Library Books on Reserve

Linear Algebra

- G. Strang,
Linear Algebra and Its Application, 4th edition (Thomson, Brooks/Cole, 2006).- P. R. Halmos,
Finite-Dimensional Vector Spaces, 2d edition (D. Van Nostrand Co., 1958).- R. A. Horn and C. R. Johnson,
Matrix Analysis(Cambridge University Press, 1985).- R. A. Horn and C. R. Johnson,
Topics in Matrix Analysis(Cambridge University Press, 1991).- S. Perlis,
Theory of Matrices, (Addison-Wesley Publishing Co., 1952).

Probability Theory

- William Feller,
An introduction to probability theory and its applicationsVol 1, 3d ed, (Wiley, 1968).- Morris H. DeGroot and Mark J. Schervish,
Probability and statistics3rd ed, (Addison-Wesley Pub. Co., 2002).- Sheldon M. Ross,
Introduction to probability models7th ed, (Harcourt/Academic Press, 2000). Other editions are also suitable.

Classical Information Theory

- T. M. Cover and J. A. Thomas,
Elements of Information Theory, 2d ed, (Wiley Interscience, 2006).

Cryptography

- D. R. Stinson,
Cryptography: Theory and Practice, 3d ed, (Chapman and Hall/CRC, 2006).

Quantum Computation and Information

- M. A. Nielsen and I. L. Chuang,
Quantum Computation and Quantum Information(Cambridge, 2000).- G. Benenti, G. Casati, G. Strini, Principles of Quantum Computation and Information. Vol. 1: Basic Concepts, Vol II: Basic Tools and Special Topics (World Scientific 2004).
- H.-K. Lo, T. Spiller, S. Popescu,
Introduction to Quantum Computation and Information(World Scientific, 1998).- N. D. Mermin, Quantum Computer Science (Cambridge, 2007).
- G. Alber et al. Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, 2001).
- A. O. Pittenger, An Introduction to Quantum Computing Algorithms (Birkhauser, 2000).

Quantum Mechanics

- C. Cohen-Tannoudji, B. Diu, F. Laloe,
Quantum Mechanics, Vols. 1, 2 (Hermann, Wiley 1977).- R. B. Griffiths,
Consistent Quantum Theory(Cambridge, 2002).- R. Omnès,
Understanding Quantum Mechanics(Princeton, 1999).- A. Peres,
Quantum Theory: Concepts and Methods, (Kluwer, 1993).- J. J. Sakurai,
Modern Quantum Mechanics, 2d ed (Addison-Wesley, 2011).- R. Shankar,
Principles of Quantum Mechanics, 2d ed (Plenum, 1994).## Computer Science

- T. H. Cormen, C. E. Leiserson and R. L. Rivest, Introduction to Algorithms (MIT Press, 1990).