Scholarlink

<p>We initiate the study of utilizing quantum Langevin dynamics (QLD) to solve optimization problems, particularly those nonconvex 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 converge to zero in the low temperature limit with an exponential convergence rate. 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 the classical Fokker-Plank-Smoluchowski equation, we propose a time-dependent QLD by setting temperature and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5234_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbar \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ħ</mi> </math></EquationSource> </InlineEquation> as 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 nonconvex landscapes.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quantum Langevin Dynamics for Optimization

  • 期刊论文

  • 发表日期：

    2025年2月17日

查看全文
  • Zherui Chen,
  • Yuchen Lu,
  • Hao Wang,
  • Yizhou Liu,
  • Tongyang Li

摘要

We initiate the study of utilizing quantum Langevin dynamics (QLD) to solve optimization problems, particularly those nonconvex 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 converge to zero in the low temperature limit with an exponential convergence rate. 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 the classical Fokker-Plank-Smoluchowski equation, we propose a time-dependent QLD by setting temperature and \(\hbar \) ħ as 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 nonconvex landscapes.