Stoquastic ground states are classical thermal distributions

TL;DR

This paper demonstrates that ground states of local stoquastic Hamiltonians can be efficiently approximated by classical distributions such as Gibbs distributions and Deep Boltzmann machines, revealing their classical simulability.

Contribution

It establishes the equivalence and efficient approximation of quantum ground states by various classical distributions under mild assumptions.

Findings

Ground states of stoquastic Hamiltonians can be approximated by classical distributions.

Classical sampling methods can efficiently simulate certain quantum states.

Deep Boltzmann machines can represent ground state distributions of stoquastic Hamiltonians.

Abstract

We study the structure of the ground states of local stoquastic Hamiltonians and show that under mild assumptions the following distributions can efficiently approximate one another: (a) distributions arising from ground states of stoquastic Hamiltonians, (b) distributions arising from ground states of stoquastic frustration-free Hamiltonians, (c) Gibbs distributions of local classical Hamiltonian, and (d) distributions represented by real-valued Deep Boltzmann machines. In addition, we highlight regimes where it is possible to efficiently classically sample from the above distributions.