Quantum nonexpander problem is quantum-Merlin-Arthur-complete
Name
Bookatz-2013-Quantum nonexpander problem.pdf
Size
253.03 KB
Format
Adobe PDF
Checksum (MD5)
535fd551c472a5614e6f303a5f079dee
Author(s)
Jordan, Stephen P.
Liu, Yi-Kai
Wocjan, Pawel
Bookatz, Adam D.
Date Issued
April 2013
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
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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevA.87.042317
