Physics 522-644
Quantum Information

Luming Duan

Fall 2010


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: Tuesday, Thursday, 9:30AM -11:00AM
 Location: 4404 Randall

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 at 4219 Randall

Course Requirements

There will be regularly assigned homework. Your letter grade is based on your class participation (10%), homework (20%), a final exam (35%), and a critique of a research paper that you choose with some guidance from me (35%).

Prerequisites

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

Books and References

Main Reference 
Books

 

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 (Preskill, chapter 2; Nielsen-Chuang Sec. 2.4, 2.5)
      • Qubit states and Bloch sphere
      • Density operator (matrix) and its properties
      • Schmidt decomposition
    3. Generalized evolution: superoperator and Kraus representation (Preskill, Chapter 3.2-3.5; Nielsen-Chuang Sec. 8.2,8.3,8.4)
      • 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 (Preskill 3.1; Nielsen-Chuang Sec. 2.2)
      • 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 (Preskill 4.1, quant-ph/9604024)
      • 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 (arxiv: quant-ph/9604024, quant-ph/9709029)
      • 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 (quant-ph/0602096;quant-ph/9604024,quant-ph/0005115)
      • 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 (Preskill 4.1.2-4.1.7)
      • 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 (Preskill 4.2)
      • Quantum teleportation
      • Dense coding
    3. Quantum key distribution (Nielsen-Chuang 12.6)
      • 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 (Preskill 5.1-5.4; Nielsen-Chuang 12.1, 12.2, 12.3, 12.4)
      • 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 (Preskill 6.1, 6.2; Nielsen-Chuang, 3.1, 4.14.6)
      • 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)

    1. Quantum algorithm 1: Deutsch-Jozsa, Grover searching, and quantum simulation (Preskill 6.3-6.6; Nielsen-Chuang 4.1,4.7, 6.1-6.7)
      • Deutsch-Jozsa algorithm
      • Grover search algorithm
      • Quantum simulation
    2. Quantum algorithm 2: Period finding and Shor's factorization (Preskill 6.9-6.12; Nielsen-Chuang 5.1-5.4)
      • 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 (Nielsen-Chuan 10.1-10.5; Preskill, Chapter 7)
      • Conditions for quantum error correction and Hamming bound
      • Stabilizer codes and examples
    3. Fault-tolerant quantum computation (Nielsen-Chuang 10.6)
      • 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 (quant-ph/9710025; quant-ph/0405030; Nielsen-Chuang 7.6)
      • 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 (quant-ph/0405030)
      • 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 (see review articles on arxiv)
    5. Quantum dot based quantum computation (cond-mat/9911245)
    6. SQUIDs based quantum computation (Rev. Mod. Phys. 73, 357-400 (2001))
    7. Quantum repeaters for communication and their implementation (quant-ph/0405030)

 Homework

    1. Solutions to Homework 1
    2. Solutions to Homework 2
    3. Solutions to Homework 3
    4. Solutions to Homework 4

Links