Published September 2007
| Version v1
Journal article
Random unitaries give quantum expanders
Creators
- 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
Identifiers
- DOI
- 10.1103/PhysRevA.76.032315;
- arXiv
- arXiv:0706.0556v1;
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