Non-convex Quadratic Programming Using Coherent Optical Networks

TL;DR

This paper explores using quantum optical networks to solve non-convex quadratic programming problems efficiently by simulating diffusion processes in continuous variables, demonstrating significant speed advantages over classical heuristics.

Contribution

It introduces a novel approach to encode and solve continuous non-convex optimization problems using quantum optical modes and demonstrates its effectiveness through numerical benchmarking.

Findings

Optical networks can solve BoxQP problems over three orders of magnitude faster than classical heuristics.

The proposed method successfully encodes continuous variables in quantum optical modes.

Different experimental variants show consistent speedup in solving quadratic programming problems.

Abstract

We investigate the possibility of solving continuous non-convex optimization problems using a network of interacting quantum optical oscillators. We propose a native encoding of continuous variables in analog signals associated with the quadrature operators of a set of quantum optical modes. Optical coupling of the modes and noise introduced by vacuum fluctuations from external reservoirs or by weak measurements of the modes are used to optically simulate a diffusion process on a set of continuous random variables. The process is run sufficiently long for it to relax into the steady state of an energy potential defined on a continuous domain. As a first demonstration, we numerically benchmark solving box-constrained quadratic programming (BoxQP) problems using these settings. We consider delay-line and measurement-feedback variants of the experiment. Our benchmarking results demonstrate that in both cases the optical network is capable of solving BoxQP problems over three orders of magnitude faster than a state-of-the-art classical heuristic.