QMA-complete problems for stoquastic Hamiltonians and Markov matrices
Quantum Physics
2013-05-29 v2
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.
Cite
@article{arxiv.0905.4755,
title = {QMA-complete problems for stoquastic Hamiltonians and Markov matrices},
author = {Stephen P. Jordan and David Gosset and Peter J. Love},
journal= {arXiv preprint arXiv:0905.4755},
year = {2013}
}
Comments
11 pages. Contains several new results not present in version 1.