Quantum-Merlin-Arthur-complete problems for stoquastic Hamiltonians and Markov matrices

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.032331· OSTI ID:21408402

Jordan, Stephen P; Gosset, David; Love, Peter J ^[1]

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1. Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)

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.

• OSTI ID: 21408402
• Journal Information: Physical Review. A, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.032331; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
EIGENVALUES
EVOLUTION
EXCITED STATES
GROUND STATES
HAMILTONIANS
MARKOV PROCESS
MATRICES
QUANTUM COMPUTERS
SYMMETRY
COMPUTERS
ENERGY LEVELS
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
STOCHASTIC PROCESSES