Swarm-like ground-state searching based on a path-integral quantum Monte Carlo method for automatically fluctuation-controlled simulated annealing

The path-integral quantum Monte Carlo (PIQMC) method is widely used as a classical simulation algorithm for quantum annealing. Replicas represent different points in imaginary time. We propose and demonstrate a swarm-like ground-state searching algorithm based on the PIQMC method for automatically fluctuation-controlled simulated annealing. Replicas help one another to search for the ground state of an Ising system as if forming a swarm and working cooperatively. Their interactions are local, simple and fluctuate to a certain degree. Such fluctuations are necessary to escape local minima, but the fluctuations do not need to be explicitly controlled. The size of fluctuations is automatically adjusted as annealing proceeds. We solve max-cut problems for algorithm evaluation, each of which corresponds to a graph of 100 vertices. We also solve the same problems using a conventional method based on the Metropolis algorithm for comparison.