Quantum nonexpander problem is quantum-Merlin-Arthur-complete

Author(s)
Jordan, Stephen P.; Liu, Yi-Kai; Wocjan, Pawel; Bookatz, Adam D.
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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 the problem of deciding whether a quantum channel is not rapidly mixing is a complete problem for the quantum Merlin-Arthur complexity class. This has applications to testing randomized constructions of quantum expanders and studying thermalization of open quantum systems.
Date issued
2013-04
URI
http://hdl.handle.net/1721.1/88738
Department
Massachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Department of Mathematics; Massachusetts Institute of Technology. Department of Physics
Journal
Physical Review A
Publisher
American Physical Society
Citation
Bookatz, Adam, Stephen Jordan, Yi-Kai Liu, and Pawel Wocjan. “Quantum Nonexpander Problem Is Quantum-Merlin-Arthur-Complete.” Phys. Rev. A 87, no. 4 (April 2013). © 2013 American Physical Society
Version: Final published version
ISSN
1050-2947
1094-1622
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