Physics 613
Quantum Information: Theory and Implementation
Luming Duan
Winter 2015
Welcome to the homepage for the Quantum
Information course.
Course Description
This course will focus on 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, 10:00AM 11:30AM
Location: 2448 Mason Hall
Instructors
Luming Duan
2448 Mason Hall
Telephone: (734) 7633179
Email: lmduan@umich.edu
Web: http://wwwpersonal.umich.edu/~lmduan/
Course website: http://wwwpersonal.umich.edu/~lmduan/QIpub.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 (40%),
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



Other
Books


 Introduction to
Quantum Computation and Information,edited by
HoiKwong 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,
quantph/0405030.
 D.J. Wineland, C. Monroe, W.M. Itano,
D. Leibfried, B.E. King, D.M. Meekhof, Experimental issues in coherent quantumstate
manipulation of trapped atomic ions, quantph/9710025.
 C. Ramanathan, N. Boulant, Z.
Chen, D. G. Cory, I. Chuang, M. Steffen, NMR Quantum Information
Processing, quantph/0408166.
 D.P. DiVincenzo, G. Burkard, D. Loss, E. V. Sukhorukov, Quantum Computation and Spin
Electronics, http://arxiv.org/abs/condmat/9911245.
 Y. Makhlin,
G. Schon, and A. Shnirman,
Quantumstate engineering with Josephsonjunction devices, Rev. Mod.
Phys. 73, 357400 (2001).

Course Outline
 Introduction
 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
 Quantum
communication: an overview
 Communication with
quantum states and teleportation
 Quantum
cryptography
 Quantum foundation:
generalized states, evolution, and measurements
 Overview of axioms
for quantum mechanics
 Density operator
and Schmidt decomposition (Preskill, chapter 2;
NielsenChuang Sec. 2.4, 2.5)
 Qubit states and
Bloch sphere
 Density operator
(matrix) and its properties
 Schmidt
decomposition
 Generalized
evolution: superoperator and Kraus
representation (Preskill, Chapter 3.23.5;
NielsenChuang Sec. 8.2,8.3,8.4)
 Superoperator
and its properties
 The Kraus theorem
and operatorsum representation
 Relation between
operatorsum and unitary representations
 Examples of superoperator evolution: quantum channels
 Generalized
measurements: POVM (Preskill 3.1;
NielsenChuang Sec. 2.2)
 Measurements in
composite systems and POVM
 Relation between
POVM and projective measurements in extended space
 Quantum entanglement
theory
 Overview
 Entanglement of
pure states and Von Neumann entropy (Preskill
4.1, quantph/9604024)
 Multipartite
systems and concept of entanglement
 Von Neumann
entropy and its properties
 Entanglement of
formation and distillation
 Multipartite
entanglement
 Entanglement
criteria and measures for mixed states (arxiv: quantph/9604024, quantph/9709029)
 Entanglement
criteria for mixed states
 Entanglement
measures for mixed states
 Expression of
entanglement of formation (concurrence) for 2qubit mixed states
 Typical entangled
states and their properties (quantph/0602096;quantph/9604024,quantph/0005115)
 Bell states, GHZ
states, and Werner states
 W states and Dicke states
 Cluster states,
and graph (stabilizer) states
 Quantum nonlocality
and Bell's inequalities (Preskill 4.1.24.1.7)
 Background
 BellCHSH
inequalities
 Maximum violation
of Bell's inequalities
 Experimental
verification and its loopholes
 Quantum communication:
teleportation and cryptography
 Overview
 Entanglement
assisted communication (Preskill 4.2)
 Quantum
teleportation
 Dense coding
 Quantum key
distribution (NielsenChuang 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
 Quantum coding
theorems (Preskill 5.15.4; NielsenChuang
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
 Overview
 Models and
structure of quantum computation (Preskill 6.1,
6.2; NielsenChuang, 3.1, 4.1—4.6)
 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)
 Quantum algorithm
1: DeutschJozsa, Grover searching, and quantum
simulation (Preskill 6.36.6; NielsenChuang
4.1,4.7, 6.16.7)
 DeutschJozsa algorithm
 Grover search
algorithm
 Quantum simulation
 Quantum algorithm
2: Period finding and Shor's factorization (Preskill
6.96.12; NielsenChuang 5.15.4)
 Quantum Fourier
transform
 Efficient period
finding through QFT
 Reduction of
factoring to period finding
 Remarks and
generalizations
 Quantum error correction
 Overview
 Quantum error
correction (NielsenChuan 10.110.5; Preskill, Chapter 7)
 Conditions for
quantum error correction and Hamming bound
 Stabilizer codes
and examples
 Faulttolerant quantum computation (NielsenChuang 10.6)
 Basic idea for
achieving fault tolerance
 Concatenation and
the error threshold theorem
 Implementation of quantum
computation and communication
 Overview
 Trapped ion quantum computation (quantph/9710025; quantph/0405030; NielsenChuang 7.6)
 Paul trap for ions
 Ion motion and
phonon modes
 Doppler and
sideband cooling for trapped ions
 Atomic level
configuration and singlebit operations
 Twobit gate
(CZMSMphase gate)
 Initial state
preparation and final state detection
 Ion trap scaling
 Neutral atom
quantum computation (quantph/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
 Photon quantum
computation (see review articles on arxiv)
 Quantum dot based
quantum computation (condmat/9911245)
 SQUIDs based
quantum computation (Rev. Mod. Phys. 73, 357400 (2001))
 Quantum repeaters
for communication and their implementation (quantph/0405030)
Homework
Links