Feedback and constraints in physical optimizers
Niharika Gunturu, Hideo Mabuchi, Edwin Ng, Daniel Wennberg, Ryotatsu Yanagimoto Β· 2024
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 π with π₯ constrained to a unit ball in π π can be performed simply by finding the maximum (principal) eigenvector of π, but can become computationally intractable if the domain of π₯ is limited to corners of the Β±1 hypercube in π π (i.e., π₯ 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.