Classical and Quantum Simulation of Stoquastic Hamiltonian Systems

Abstract

Quantum systems are in general not e_ciently simulatable by classical means. If one wishes to determine (some of) the eigenvalues of a Hamiltonian H that is associated with a quantum system, there are two favoured strategies: Quantum simulation and quantum Monte Carlo schemes. The former strategy uses an experimentally well-controllable quantum system that emulates the system of interest, in a digital (i.e. universal) or analog manner. The latter, albeit with a limited range of applicability, uses classical stochastic processes to e_ciently obtain (often low-lying) eigenvalues of H. Quantum Monte Carlo methods may su_er from a sign problem when simulating fermionic or frustrated bosonic systems. This yields, for a given accuracy, a simulation time that scales exponentially in the system size and the inverse temperature.