Random Unitaries Give Quantum Expanders - Quantum PhysicsReport as inadecuate

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

Author: M. B. Hastings

Source: https://arxiv.org/

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