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arXiv · 1210.0787

Testing quantum expanders is co-QMA-complete

Adam D. Bookatz·Stephen P. Jordan·Yi-Kai Liu·Pawel Wocjan
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Abstract

A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is co-QMA-complete. This has applications to testing randomized constructions of quantum expanders, and studying thermalization of open quantum systems.

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Adam D. Bookatz, Stephen P. Jordan, Yi-Kai Liu, Pawel Wocjan. 2013-05-31. Testing quantum expanders is co-QMA-complete. https://doi.org/10.1103/physreva.87.042317

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