Random Unitaries Give Quantum Expanders
Quantum Physics
2009-11-13 v1 Strongly Correlated Electrons
Abstract
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.
Cite
@article{arxiv.0706.0556,
title = {Random Unitaries Give Quantum Expanders},
author = {M. B. Hastings},
journal= {arXiv preprint arXiv:0706.0556},
year = {2009}
}