We initiate the study of utilizing Quantum Langevin Dynamics (QLD) to solve optimization problems, particularly those non-convex objective functions that present substantial obstacles for traditional gradient descent algorithms. Specifically, we examine the dynamics of a system coupled with an infinite heat bath. This interaction induces both random quantum noise and a deterministic damping effect to the system, which nudge the system towards a steady state that hovers near the global minimum of objective functions. We theoretically prove the convergence of QLD in convex landscapes, demonstrating that the average energy of the system can approach zero in the low temperature limit with an exponential decay rate correlated with the evolution time. Numerically, we first show the energy dissipation capability of QLD by retracing its origins to spontaneous emission. Furthermore, we conduct detailed discussion of the impact of each parameter. Finally, based on the observations when comparing QLD with classical Fokker-Plank-Smoluchowski equation, we propose a time-dependent QLD by making temperature and $\hbar$ time-dependent parameters, which can be theoretically proven to converge better than the time-independent case and also outperforms a series of state-of-the-art quantum and classical optimization algorithms in many non-convex landscapes.

翻译：我们率先研究了利用量子朗之万动力学（QLD）求解优化问题，特别是那些给传统梯度下降算法带来重大障碍的非凸目标函数。具体而言，我们考察了一个与无限热浴耦合的系统的动力学过程。这种耦合相互作用向系统同时引入了随机量子噪声和确定性阻尼效应，促使系统趋向于一个徘徊在目标函数全局最小值附近的稳态。我们从理论上证明了QLD在凸景观中的收敛性，表明在低温极限下，系统的平均能量能够以与演化时间相关的指数衰减速率趋近于零。在数值实验方面，我们首先通过追溯QLD的起源——自发辐射，展示了其能量耗散能力。此外，我们详细讨论了每个参数的影响。最后，基于QLD与经典Fokker-Plank-Smoluchowski方程对比时的观测结果，我们提出了一种时间依赖型QLD：将温度和 ℏ 设为时间依赖参数。理论上可证明其收敛性能优于时间无关情形，并且在多种非凸景观中胜出了一系列最先进的量子与经典优化算法。