Physics 522-644
Quantum Information

Luming Duan

Fall 2005

Welcome to the homepage for the course of Quantum Information and Atomic Physics! This is a graduate-level course.

Course Description

This course will focus on theory of quantum information and its implementation. It will cover the following topics: quantum entanglement theory, quantum communication and cryptography, Quantum Shannon theory, quantum computation and algorithms, quantum error correction, implementation of quantum computation and communication.

Class meetings

 Time: Monday, Wednesday, 2:30PM -4:00PM
 Location: 229 Dennison

Instructors

Luming Duan
4219 Randall Hall
Telephone: (734) 763-3179
Email: lmduan@umich.edu
Web: http://www-personal.umich.edu/~lmduan/
Course website: http://www-personal.umich.edu/~lmduan/QI-pub.html

Office hours: Just stop by my office

Course Requirements

There will be regularly assigned homework. Your letter grade is based on your class participation (10%), homework (30%), a final exam (30%), and a critique of a research paper that you choose with some guidance from me (30%).

Prerequisites

It is helpful to have a previous course on quantum mechanics.

Books and References

Main Reference  Books		John Preskill, Lecture Notes on quantum inforamtion and computation http://www.theory.caltech.edu/people/preskill/ph229/#lecture M. A. Nielsen, I. L. Chuang. Quantum Computation and Quantum Information  Cambridge Press (2000)
Other  Books		Introduction to Quantum Computation and Information,edited by Hoi-Kwong Lo et al (2001)  The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation, edited by Dirk Bouwmeester et al (2000)  Quantum Information with Continuous Variables, edited by S.L. Braunstein, A.K. Pati Experimental Quantum Computation and Information (International School of Physics ""Enrico Fermi"", 148) by F. De Martini (Editor) (2002)  Classical and Quantum Computation,by A. Yu. Kitaev, et al (2002)  Quantum Entanglement and Information Processing : Proceedings of the Les Houches Summer School 2003 (Les Houches) by Daniel Est?e, et al (2004)  Lectures on Quantum Information by D Bruss (2006)
Some Review  articles on implementation		J. I. Cirac, L. M. Duan, P. Zoller, Quantum optical implementation of quantum information processing, quant-ph/0405030. D.J. Wineland, C. Monroe, W.M. Itano, D. Leibfried, B.E. King, D.M. Meekhof, Experimental issues in coherent quantum-state manipulation of trapped atomic ions, quant-ph/9710025.  C. Ramanathan, N. Boulant, Z. Chen, D. G. Cory, I. Chuang, M. Steffen, NMR Quantum Information Processing, quant-ph/0408166. D.P. DiVincenzo, G. Burkard, D. Loss, E. V. Sukhorukov, Quantum Computation and Spin Electronics, http://arxiv.org/abs/cond-mat/9911245. Y. Makhlin, G. Schon, and A. Shnirman, Quantum-state engineering with Josephson-junction devices, Rev. Mod. Phys. 73, 357-400 (2001).

Course Outline

• Introduction
1. Quantum computation: an overview of history and recent developments
• Limit of classical computation
• Reversible and quantum computation
• Quantum algorithms and quantum simulation
• Construction of quantum computers: Universality Theorem & Threshold Theorem
• Implementation of quantum computation
2. Quantum communication: an overview
• Communication with quantum states and teleportation
• Quantum cryptography
• Quantum foundation: generalized states, evolution, and measurements
1. Overview of axioms for quantum mechanics
2. Density operator and Schmidt decomposition
• Qubit states and Bloch sphere
• Density operator (matrix) and its properties
• Schmidt decomposition
3. Generalized evolution: superoperator and Kraus representation
• Superoperator and its properties
• The Kraus theorem and operator-sum representation
• Relation between operator-sum and unitary representations
• Examples of superoperator evolution: quantum channels
4. Generalized measurements: POVM
• Measurements in composite systems and POVM
• Relation between POVM and projective measurements in extended space

• Quantum entanglement theory
1. Overview
2. Entanglement of pure states and Von Neumann entropy
• Multi-partite systems and concept of entanglement
• Von Neumann entropy and its properties
• Entanglement of formation and distillation
• Multi-partite entanglement
3. Entanglement criteria and measures for mixed states
• Entanglement criteria for mixed states
• Entanglement measures for mixed states
• Expression of entanglement of formation (concurrence) for 2-qubit mixed states
4. Typical entangled states and their properties
• Bell states, GHZ states, and Werner states
• W states and Dicke states
• Cluster states, and graph (stabilizer) states
5. Quantum nonlocality and Bell's inequalities
• Background
• Bell-CHSH inequalities
• Maximum violation of Bell's inequalities
• Experimental verification and its loopholes
• Quantum communication: teleportation and cryptography
1. Overview
2. Entanglement assisted communication
• Quantum teleportation
• Dense coding
3. Quantum key distribution
• The basic idea
• How to establish a key: the BB84 protocol
• Analysis of noise and eavesdropping
• Proof of the security
• Other protocols
• Quantum cloning
4. Quantum coding theorems
• The Holevo bound
• Classical and quantum data compression
• Classical and quantum capacities of quantum channels
• Quantum computation and algorithms
1. Overview
2. Models and structure of quantum computation
• Classical circuit model and computation complexity
• Basic requirements of quantum computation
• Elementary quantum gates
• Universality theorem
• Gate simulation efficiency and quantum computation complexity
• Other models of quantum computation
        -- (Quantum Turing machine, graph state model, and measurement based computation)
3. Quantum algorithm 1: Deutsch-Jozsa, Grover searching, and quantum simulation
• Deutsch-Jozsa algorithm
• Grover search algorithm
• Quantum simulation
4. Quantum algorithm 2: Period finding and Shor's factorization
• Quantum Fourier transform
• Efficient period finding through QFT
• Reduction of factoring to period finding
• Remarks and generalizations
• Quantum error correction
1. Overview
2. Quantum error correction
• Conditions for quantum error correction and Hamming bound
• Stabilizer codes and examples
3. Fault-tolerant quantum computation
• Basic idea for achieving fault tolerance
• Concatenation and the error threshold theorem
• Implementation of quantum computation and communication
1. Overview
2. Trapped ion quantum computation
• Paul trap for ions
• Ion motion and phonon modes
• Doppler and sideband cooling for trapped ions
• Atomic level configuration and single-bit operations
• Two-bit gate (CZ-MSM-phase gate)
• Initial state preparation and final state detection
• Ion trap scaling
3. Neutral atom quantum computation
• Neutral atoms in optical lattice
• Gate based on collision interaction
• Gate based on dipole blockade with Rydberg level excitation
• Gate based on cavity assisted photon interaction
4. Photon quantum computation
5. Quantum dot based quantum computation
6. SQUIDs based quantum computation
7. Quantum repeaters for communication and their implementation

 

Links

• Physics department of the University of Michigan.
• Luming Duan's Homepage