Monte Carlo Quantum Computing

TL;DR

This paper demonstrates that certain frustration-free Hamiltonians can be efficiently simulated classically using Monte Carlo methods, effectively addressing the sign problem and linking quantum algorithms to classical probabilistic simulations.

Contribution

It introduces a class of frustration-free Hamiltonians that are efficiently simulatable and shows they can implement universal quantum computation, bridging quantum and classical computational models.

Findings

Efficient Monte Carlo simulation of SFF Hamiltonians

Solution to the sign problem in Monte Carlo methods

Universal quantum computation via designed Hamiltonians

Abstract

It is shown that a class of separately frustration-free (SFF) Hamiltonians can be Monte Carlo simulated efficiently on a classical computing machine, because such an SFF Hamiltonian corresponds to a Gibbs wavefunction whose nodal structure is efficiently computable by solving a small subsystem associated with a low-dimensional configuration subspace. It is further demonstrated that SFF Hamiltonians can be designed to implement universal ground state quantum computation. The two results combined have effectively solved the notorious sign problem in Monte Carlo simulations, and proved that all bounded-error quantum polynomial time algorithms admit bounded-error probabilistic polynomial time simulations.