Quantum Monte Carlo simulation of a particular class of non-stoquastic Hamiltonians in quantum annealing
This addresses a computational bottleneck for researchers simulating quantum annealing with non-stoquastic Hamiltonians, but it is incremental as it focuses on a particular class of problems.
The authors tackled the negative sign problem in quantum Monte Carlo simulations of quantum annealing for non-stoquastic Hamiltonians by proposing an alternative method to avoid it, demonstrating its validity on a simple problem with anti-ferromagnetic XX interactions.
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.