Computational Speedup of Simulated Annealing with Nested Monte Carlo Loop

An Ising spin model interacting with neighboring spins has been eagerly studied along with the progress in Quantum Computing (QC). Quantum Monte Carlo (QMC) is often used in simulation, but it is such a heuristic approach that it has great difficulty in that it takes a long time to solve the problem. It mainly depends on the existence of a trotter layer derived from Suzuki-Trotter decomposition. In my previous work, I proposed a new approach to compute it much faster by changing the order in which all energies over the trotter layer are summed and minimized. In the algorithm, a plural of trotter layers could be treated in parallel and Time to Solution (TTS) could be reduced as well as that of Simulated Annealing (SA), although it requires a lot of computational resources.In this paper, in order to balance them, a new approach is proposed, where the number of inner loops is not changed but the number of the trotter layers is smaller. With such a small trotter loop repeated in several times, the proposed method works as so-called partial optimization and it leads to very fast convergence. Moreover, it doesn’t affect the result whether the updating spins are the same or not during the partial optimization. This fact also indicates that the new method would open another door to parallel computation. These results are verified by solving MaxCut problem, GSET.