Combinatorial optimization problems are prevalent in various fields, but obtaining exact solutions remains challenging due to the combinatorial explosion with increasing problem size. Special-purpose hardware such as Ising machines, particularly memristor-based analog Ising machines, have emerged as promising solutions. However, existing simulate-annealing-based implementations have not fully exploited the inherent parallelism and analog storage/processing features of memristor crossbar arrays. This work proposes a quantum-inspired parallel annealing method that enables full parallelism and improves solution quality, resulting in significant speed and energy improvement when implemented in analog memristor crossbars. We experimentally solved tasks, including unweighted and weighted Max-Cut and traveling salesman problem, using our integrated memristor chip. The quantum-inspired parallel annealing method implemented in memristor-based hardware has demonstrated significant improvements in time- and energy-efficiency compared to previously reported simulated annealing and Ising machine implemented on other technologies. This is because our approach effectively exploits the natural parallelism, analog conductance states, and all-to-all connection provided by memristor technology, promising its potential for solving complex optimization problems with greater efficiency.

组合优化问题在各个领域都很普遍，但由于问题规模的增加导致组合爆炸，获得精确的解决方案仍然具有挑战性。诸如伊辛机之类的专用硬件，特别是基于忆阻器的模拟伊辛机，已成为有前途的解决方案。然而，现有的基于模拟退火的实现尚未充分利用忆阻器交叉阵列固有的并行性和模拟存储/处理功能。这项工作提出了一种受量子启发的并行退火方法，该方法可实现完全并行并提高解决方案质量，从而在模拟忆阻器交叉开关中实现时显着提高速度和能耗。我们使用我们的集成忆阻器芯片实验性地解决了任务，包括未加权和加权 Max-Cut 以及旅行商问题。与之前报道的基于其他技术实现的模拟退火和伊辛机相比，在基于忆阻器的硬件中实现的量子启发并行退火方法在时间和能源效率方面表现出显着的改进。这是因为我们的方法有效地利用了忆阻器技术提供的自然并行性、模拟电导状态和全对全连接，有望以更高的效率解决复杂的优化问题。