Message-passing algorithm of quantum annealing with nonstoquastic Hamiltonian
This provides a new classical simulation approach for quantum annealing, addressing a bottleneck in evaluating nonstoquastic systems, though it is incremental as it builds on prior work for fully connected models.
The paper tackled the problem of simulating quantum annealing with nonstoquastic Hamiltonians, which are not classically simulatable by standard methods, by developing a message-passing algorithm that assesses performance for large spin systems without using quantum Monte Carlo, validated against replica method results.
Quantum annealing (QA) is a generic method for solving optimization problems using fictitious quantum fluctuation. The current device performing QA involves controlling the transverse field; it is classically simulatable by using the standard technique for mapping the quantum spin systems to the classical ones. In this sense, the current system for QA is not powerful despite utilizing quantum fluctuation. Hence, we developed a system with a time-dependent Hamiltonian consisting of a combination of the formulated Ising model and the "driver" Hamiltonian with only quantum fluctuation. In the previous study, for a fully connected spin model, quantum fluctuation can be addressed in a relatively simple way. We proved that the fully connected antiferromagnetic interaction can be transformed into a fluctuating transverse field and is thus classically simulatable at sufficiently low temperatures. Using the fluctuating transverse field, we established several ways to simulate part of the nonstoquastic Hamiltonian on classical computers. We formulated a message-passing algorithm in the present study. This algorithm is capable of assessing the performance of QA with part of the nonstoquastic Hamiltonian having a large number of spins. In other words, we developed a different approach for simulating the nonstoquastic Hamiltonian without using the quantum Monte Carlo technique. Our results were validated by comparison to the results obtained by the replica method.