Sign-problem free quantum stochastic series expansion algorithm on a quantum computer

Abstract

A quantum implementation of the Stochastic Series Expansion (SSE) Monte Carlo method is proposed, and is shown to offer significant advantages over classical implementations of SSE. In particular, for problems where classical SSE encounters the sign problem, the cost of implementing a Monte Carlo iteration scales only linearly with system size in quantum SSE, while it may scale exponentially with system size in classical SSE. In cases where classical SSE can be efficiently implemented, quantum SSE still offers an advantage by allowing for more general observables to be measured.