Random Unitaries Give Quantum Expanders

Details Random Unitaries Give Quantum Expanders Random Unitaries Give Quantum Expanders

2007-06-05

arxiv.org/abs/0706.0556v1

Phys. Rev. A 76, 032315 (2007).

Physics

Quantum Physics

14 pages, 1 figure

Scientific paper

10.1103/PhysRevA.76.032315

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.

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