Two-local qubit Hamiltonians: when are they stoquastic?

TL;DR

This paper investigates when two-qubit Hamiltonians can be made stoquastic through local basis changes, providing tools, examples, and an efficient algorithm for certain classes of Hamiltonians.

Contribution

It introduces an efficient algorithm to determine stoquasticity of n-qubit XYZ Heisenberg Hamiltonians via local basis transformations.

Findings

An example requiring non-Clifford unitaries for stoquasticity.

Simple results for n-qubit Hamiltonians with identical 2-local terms.

An efficient algorithm for XYZ Heisenberg Hamiltonians.

Abstract

We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquasticity. We report on simple results for $n$-qubit Hamiltonians with identical 2-local terms on bipartite graphs. Our most significant result is that we give an efficient algorithm to determine whether an arbitrary $n$-qubit XYZ Heisenberg Hamiltonian is stoquastic by local basis changes.