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arXiv · 0905.4755

QMA-complete problems for stoquastic Hamiltonians and Markov matrices

Stephen P. Jordan·David Gosset·Peter J. Love
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Abstract

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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Stephen P. Jordan, David Gosset, Peter J. Love. 2010-03-29. QMA-complete problems for stoquastic Hamiltonians and Markov matrices. https://doi.org/10.1103/physreva.81.032331

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