  In this paper, we introduce stochastic simulated quantum annealing (SSQA) for
large-scale combinatorial optimization problems. SSQA is designed based on
stochastic computing and quantum Monte Carlo, which can simulate quantum
annealing (QA) by using multiple replicas of spins (probabilistic bits) in
classical computing. The use of stochastic computing leads to an efficient
parallel spin-state update algorithm, enabling quick search for a solution
around the global minimum energy. Therefore, SSQA realizes quantum-like
annealing for large-scale problems and can handle fully connected models in
combinatorial optimization, unlike QA. The proposed method is evaluated in
MATLAB on graph isomorphism problems, which are typical combinatorial
optimization problems. The proposed method achieves a convergence speed an
order of magnitude faster than a conventional stochastic simulaated annealing
method. Additionally, it can handle a 100-times larger problem size compared to
QA and a 25-times larger problem size compared to a traditional SA method,
respectively, for similar convergence probabilities.
