Quantum-Merlin-Arthur-complete problems for stoquastic Hamiltonians and Markov matrices
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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.
Date issued
2010-03Department
Massachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Department of PhysicsJournal
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
ISSN
1050-2947
1094-1622