Discrete Polynomial Optimization with Coherent Networks of Condensates and Complex Coupling Switching

TL;DR

This paper demonstrates how networks of nonequilibrium condensates can be used to solve complex discrete polynomial optimization problems by implementing higher-order Hamiltonians and utilizing complex coupling switching for efficient solution finding.

Contribution

It introduces a novel approach to realize k-local Hamiltonians with condensate networks and shows how complex couplings enhance the search for global solutions in large-scale problems.

Findings

Networks can realize k-local Hamiltonians with k>2.

Complex couplings improve the efficiency of solution search.

Method demonstrated on tensors with millions of entries.

Abstract

Gain-dissipative platforms consisting of lasers, optical parametric oscillators and nonequilibrium condensates operating at the condensation/coherence threshold have been recently proposed as efficient analog simulators of 2-local spin Hamiltonians with continuous or discrete degrees of freedom. We show that nonequilibrium condensates above the threshold arranged in an interacting network may realise k-local Hamiltonians with k>2 and lead to nontrivial phase configurations. The principle of the operation of such a system lays the ground for physics-inspired computing and the new efficient methods for finding solutions to the higher order binary optimization problems. We show how to facilitate the search for the global solution by invoking complex couplings in the system and demonstrate the efficiency of the method on tensors with million entries. This approach offers a highly flexible new kind of computation based on gain-dissipative simulators with complex coupling switching. g.