Feedback and constraints in physical optimizers
Feedback and constraints in physical optimizers
复制标题
物理优化器中的反馈和约束
DOI：
10.1117/12.3005007
复制
发表时间：
2024
期刊：
影响因子：
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通讯作者：
Yanagimoto, Ryotatsu
中科院分区：
文献类型：
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作者：
Gunturu, Niharika;Mabuchi, Hideo;Ng, Edwin;Wennberg, Daniel;Yanagimoto, Ryotatsu
二次形式的优化在计算上可以是简单的，也可以是困难的，这取决于优化变量的可行域。例如，对于实对称矩阵E，最大化E = xTVx，其中E被约束到单位球，可以简单地通过找到E的最大（主）特征向量来执行，但是如果E的域被限制到±1超立方体的角，则可能在计算上变得难以处理（即，𝑅𝑁将其约束为二进制向量）。许多增益-损耗物理系统，如相干耦合的激光器阵列或光学参量振荡器，自然地解决了最小/最大本征向量问题（耦合系数矩阵）在其平衡动力学。在本文中，我们讨论了最近的案例研究，使用添加的非线性动力学和实时反馈，在这样的系统中执行约束，使他们潜在的有用的解决困难的优化问题。我们考虑的例子在经典和量子制度的操作。
Extremizing a quadratic form can be computationally straightforward or difficult depending on the feasible domain over which variables are optimized. For example, maximizing E = xTVx for a real-symmetric matrix 𝑉 with 𝑥 constrained to a unit ball in 𝑅𝑁can be performed simply by finding the maximum (principal) eigenvector of 𝑉, but can become computationally intractable if the domain of 𝑥 is limited to corners of the ±1 hypercube in 𝑅𝑁(i.e., 𝑥 is constrained to be a binary vector). Many gain-loss physical systems, such as coherently coupled arrays of lasers or optical parametric oscillators, naturally solve minimum/maximum eigenvector problems (of a matrix of coupling coefficients) in their equilibration dynamics. In this paper we discuss recent case studies on the use of added nonlinear dynamics and real-time feedback to enforce constraints in such systems, making them potentially useful for solving difficult optimization problems. We consider examples in both classical and quantum regimes of operation.