QMA-complete problems for stoquastic Hamiltonians and Markov matrices

Details QMA-complete problems for stoquastic Hamiltonians and Markov matrices QMA-complete problems for stoquastic Hamiltonians and Markov matrices

2009-05-28

arxiv.org/abs/0905.4755v2

Phys. Rev. A 81(3), 032331 (2010)

Physics

Quantum Physics

11 pages. Contains several new results not present in version 1.

Scientific paper

We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is 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 new QMA-complete problem arising in the classical setting of Markov chains, and new adiabatically universal Hamiltonians that arise in many physical systems.

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