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arXiv · 0706.0556

Random Unitaries Give Quantum Expanders

M. B. Hastings
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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.

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M. B. Hastings. 2007-06-05. Random Unitaries Give Quantum Expanders. https://doi.org/10.1103/physreva.76.032315

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