Quantum nonexpander problem is quantum-Merlin-Arthur-complete

• Main Authors: Jordan, Stephen P. (Author), Liu, Yi-Kai (Author), Wocjan, Pawel (Contributor), Bookatz, Adam D. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Center for Theoretical Physics (Contributor), Massachusetts Institute of Technology. Department of Mathematics (Contributor), Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2014-08-15T18:29:29Z.
• Subjects: Article
• Online Access: Get fulltext

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.
United States. Dept. of Energy (Cooperative Research Agreement DE-FG02-05ER41360)
National Science Foundation (U.S.). Center for Science of Information (Grant CCF-0939370)
National Science Foundation (U.S.) (CAREER Award CCF-0746600)