Quantum Annealing via Path-Integral Monte Carlo with Data Augmentation

This paper considers quantum annealing in the Ising framework for solving combinatorial optimization problems. The path-integral Monte Carlo simulation approach is often used to approximate quantum annealing and implement the approximation by classical computers, which refers to simulated quantum annealing. In this paper we introduce a data augmentation scheme into simulated quantum annealing and develop a new algorithm for its implementation. The proposed algorithm reveals new insights on the sampling behaviors in simulated quantum annealing. Theoretical analyses are established to justify the algorithm, and numerical studies are conducted to check its performance and to confirm the theoretical findings.