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Quantum annealing (QA) is a generic method for solving optimization problemsusing fictitious quantum fluctuation. The current device performing QA involvescontrolling the transverse field; it is classically simulatable by using thestandard technique for mapping the quantum spin systems to the classical ones.In this sense, the current system for QA is not powerful despite utilizingquantum fluctuation. Hence, we developed a system with a time-dependentHamiltonian consisting of a combination of the formulated Ising model and the"driver" Hamiltonian with only quantum fluctuation. In the previous study, fora fully connected spin model, quantum fluctuation can be addressed in arelatively simple way. We proved that the fully connected antiferromagneticinteraction can be transformed into a fluctuating transverse field and is thusclassically simulatable at sufficiently low temperatures. Using the fluctuatingtransverse field, we established several ways to simulate part of thenonstoquastic Hamiltonian on classical computers. We formulated amessage-passing algorithm in the present study. This algorithm is capable ofassessing the performance of QA with part of the nonstoquastic Hamiltonianhaving a large number of spins. In other words, we developed a differentapproach for simulating the nonstoquastic Hamiltonian without using the quantumMonte Carlo technique. Our results were validated by comparison to the resultsobtained by the replica method.

Message-passing algorithm of quantum annealing with nonstoquastic Hamiltonian