Quantum Monte Carlo simulation of a particular class of non-stoquastic Hamiltonians in quantum annealing

TL;DR

This paper proposes a new method to avoid the negative sign problem in classical simulations of certain non-stoquastic Hamiltonians used in quantum annealing, demonstrated on a simple anti-ferromagnetic XX interaction problem.

Contribution

The study introduces an alternative approach to circumvent the negative sign problem in simulating specific non-stoquastic Hamiltonians in quantum annealing.

Findings

Successfully applied the method to a simple anti-ferromagnetic XX interaction problem.

Demonstrated the method's effectiveness in avoiding the negative sign problem.

Provides a potential pathway for more efficient classical simulation of non-stoquastic Hamiltonians.

Abstract

Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki--Trotter decomposition. However, the negative sign problem sometimes emerges in the simulation of quantum annealing with an elaborate driver Hamiltonian, since it belongs to a class of non-stoquastic Hamiltonians. In the present study, we propose an alternative way to avoid the negative sign problem involved in a particular class of the non-stoquastic Hamiltonians. To check the validity of the method, we demonstrate our method by applying it to a simple problem that includes the anti-ferromagnetic XX interaction, which is a typical instance of the non-stoquastic Hamiltonians.