Abstract

Finding the lowest energy of a Hamiltonian is a hard problem in general, however for many physical systems quantum Monte Carlo methods can often be effectively applied to determine the lowest energy of a Hamiltonian, and it is commonly understood that the absence of a sign problem is a requisite condition for the success of these methods. The notion of stoquastic Hamiltonians was introduced with the aim of categorizing those Hamiltonians which do not suffer from the sign problem. Indeed, the study of stoquastic Hamiltonians in the context of computational complexity theory has lent support to the notion that stoquastic Hamiltonians are somehow “simpler” than generic Hamiltonians. Importantly, the property of being stoquastic makes itself manifest only in a particular basis choice. In this work we explore how hard it is, from a computational complexity perspective, to find such a choice of basis. I will present an outline of an efficient algorithm for deciding if a 2-local Hamiltonian, with no 1-local terms, is stoquastic in some local basis.