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.

利用量子朗之万动力学 (QLD) 解决优化问题，特别是对传统梯度下降算法的障碍较大的非凸目标函数进行研究，证明了在凸景观中 QLD 的收敛性，通过数值实验和与传统算法的比较，提出了一种优于其他算法的时间相关的 QLD 算法。