Quantum-Merlin-Arthur-complete problems for stoquastic Hamiltonians and Markov matrices
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Jordan-2010-Quantum-Merlin-Arthu.pdf
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Author(s)
Gosset, David Nicholas
Love, Peter J.
Jordan, Stephen P.
Date Issued
March 2010
Journal
Physical Review A
Publisher
American Physical Society
Citation
Jordan, Stephen P. and Gosset, David and Love, Peter J. (2010). Quantum-Merlin-Arthur--complete problems for stoquastic Hamiltonians and Markov matrices. Phys. Rev. A. 81: 032331/1-10. © 2010 The American Physical Society
Version
Final published version
Abstract
We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is Quantum-Merlin-Arthur-complete (QMA-complete). We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using certain excited states of a stoquastic Hamiltonian is universal. We also show that adiabatic evolution in the ground state of a stochastic frustration-free Hamiltonian is universal. Our results give a QMA-complete problem arising in the classical setting of Markov chains and adiabatically universal Hamiltonians that arise in many physical systems.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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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.
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.81.032331
