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Testing quantum expanders is co-QMA-complete

Published

Author(s)

Yi-Kai Liu, Stephen P. Jordan, Pawel Wocjan, Adam Bookatz

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.
Citation
Theory of Computing Systems

Keywords

Computational complexity, quantum information, quantum expanders, mixing time, thermalization

Citation

Liu, Y. , Jordan, S. , Wocjan, P. and Bookatz, A. (2013), Testing quantum expanders is co-QMA-complete, Theory of Computing Systems, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=912561 (Accessed November 29, 2023)
Created May 31, 2013, Updated February 19, 2017