Networks of non-equilibrium condensates for global optimization

TL;DR

This paper presents a method to enhance networks of non-equilibrium condensates, enabling them to solve large-scale NP-hard optimization problems through a feedback mechanism that dynamically adjusts system parameters.

Contribution

It introduces a feedback-based approach to adapt gain and coupling in condensate networks, broadening their applicability to complex optimization tasks.

Findings

Proposes a feedback mechanism for parameter adjustment in condensate networks.

Demonstrates applicability to large-scale NP-hard optimization problems.

Provides principles for implementing such simulators in practice.

Abstract

Recently several gain-dissipative platforms based on the networks of optical parametric oscillators, lasers, and various non-equilibrium Bose-Einstein condensates have been proposed and realised as analogue Hamiltonian simulators for solving large-scale hard optimisation problems. However, in these realisations the parameters of the problem depend on the node occupancies that are not known a priori, which limits the applicability of the gain-dissipative simulators to the classes of problems easily solvable by classical computations. We show how to overcome this difficulty and formulate the principles of operation of such simulators for solving the NP-hard large-scale optimisation problems such as constant modulus continuous quadratic optimisation and quadratic binary optimisation for any general matrix. To solve such problems any gain-dissipative simulator has to implement a feedback mechanism for the dynamical adjustment of the gain and coupling strengths.