Published September 2007 | Version v1
Journal article

Random unitaries give quantum expanders

  • 1. Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

Description

We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the typical value of the second largest eigenvalue. The key idea is the use of Schwinger-Dyson equations from lattice gauge theory to efficiently compute averages over the unitary group

Additional details

Publishing Information

Journal Title
Physical Review. A
Journal Volume
76
Journal Issue
3
Journal Page Range
p. 032315-032315.11
ISSN
1050-2947
CODEN
PLRAAN

INIS

Country of Publication
United States
Country of Input or Organization
International Atomic Energy Agency (IAEA)
INIS RN
39038161
Subject category
S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
Descriptors DEI
EIGENFUNCTIONS; EIGENVALUES; EQUATIONS; GAUGE INVARIANCE; HERMITIAN OPERATORS; MATRICES; RANDOMNESS
Descriptors DEC
FUNCTIONS; INVARIANCE PRINCIPLES; MATHEMATICAL OPERATORS

Optional Information

Notes
(c) 2007 The American Physical Society