Solving NP-hard problems with bistable polaritonic networks

TL;DR

This paper proposes using bistable polaritonic networks to simulate Ising models and solve NP-hard optimization problems, demonstrating potential advantages over classical methods in complexity and scalability.

Contribution

It introduces a novel polaritonic network architecture for efficiently simulating Ising models and solving NP-hard problems like graph partitioning and knapsack.

Findings

The polaritonic network effectively simulates the Ising model.

Performance benchmarks show promising scaling with system size.

Potential for improved solutions in NP-hard problems.

Abstract

A lattice of locally bistable driven-dissipative cavity polaritons is found theoretically to effectively simulate the Ising model, also enabling an effective transverse field. We benchmark the system performance for spin glass problems, and study the scaling of the ground state energy deviation and success probability as a function of system size. As particular examples we consider NP-hard problems embedded in the Ising model, namely graph partitioning and the knapsack problem. We find that locally bistable polariton networks act as classical simulators for solving optimization problems, which can potentially present an improvement within the exponential complexity class.