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：我们率先研究利用量子朗之万动力学（QLD）求解优化问题，特别是那些对传统梯度下降算法构成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库耦合系统的动力学特性。这种相互作用会在系统中引入随机量子噪声与确定性阻尼效应，促使系统趋向于一个在目标函数全局最小值附近徘徊的稳态。我们从理论上证明了QLD在凸优化景观中的收敛性，表明在低温极限下系统平均能量能以与演化时间相关的指数衰减速率趋近于零。在数值实验中，我们首先通过追溯QLD的自发辐射起源展示了其能量耗散能力，进而详细讨论了各参数的影响。最后，基于QLD与经典Fokker-Plank-Smoluchowski方程比较的观察结果，我们提出将温度与量纲约化普朗克常数$ℏ$设为时变参数的时间依赖型QLD。理论证明其收敛性优于时间无关情形，并在多种非凸优化景观中超越了一系列最先进的量子与经典优化算法。