Benchmark study of simulated quantum annealing and asynchronous parallel simulated annealing for quadratic unconstrained binary optimization-based semiprime factorization

Simulated quantum annealing (SQA) has been widely studied as a heuristic for solving hard optimization problems, including integer factorization formulated as a quadratic unconstrained binary optimization (QUBO) problem. In this work, we present a replication-oriented benchmark of annealing-based solvers applied to biprime factorization using the direct QUBO mapping. We perform a controlled comparison of SQA, implemented via path-integral Monte Carlo, simulated annealing (SA), and asynchronous parallel simulated annealing (A-PSA), evaluating their performance in terms of probability of success and time to solution. Here, A-PSA denotes a multistart strategy consisting of multiple independent SA trajectories with no inter-replica interactions. Solver and encoding parameters are systematically optimized using Bayesian optimization to ensure a fair and reproducible comparison. Our results reproduce previously reported performance trends: SQA outperforms conventional SA on the considered QUBO landscapes, while SQA and A-PSA can exhibit closely comparable performance in specific regimes, highlighting the importance of multistart baselines in annealing-based benchmarking. All simulations are performed on commodity multithreaded CPU hardware using open-source software, enabling straightforward reproducibility without reliance on specialized experimental platforms. As a reference benchmark, the largest semiprime successfully factorized in our study is <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>8</a:mn> <a:mspace width="0.16em"/> <a:mn>219</a:mn> <a:mspace width="0.16em"/> <a:mn>999</a:mn> <a:mo>=</a:mo> <a:mn>32</a:mn> <a:mspace width="0.16em"/> <a:mn>749</a:mn> <a:mo>×</a:mo> <a:mn>251</a:mn> </a:mrow> </a:math> , matching results previously obtained using quantum annealing hardware.