Solving NP-hard problems with bistable polaritonic networks

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.

arXiv comment6+5 pages, 5+8 figures

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Cited by in corpus (14)

• Non-reciprocal transport of Exciton-Polaritons in a non-Hermitian chain
• Universal power law decay in the dynamic hysteresis of an optical cavity with non-instantaneous photon-photon interactions
• Tunable optical nonlinearity for TMD polaritons dressed by a Fermi sea
• Machine learning of phase transitions in nonlinear polariton lattices
• Microscopic theory of exciton and trion polaritons in doped monolayers of transition metal dichalcogenides
• Classical critical dynamics in quadratically driven Kerr resonators
• Spin-polarized antichiral exciton-polariton edge states
• Solving the max-3-cut problem using synchronized dissipative networks
• Analogue Spin Simulators: How to keep the Amplitude Homogeneous
• Lower bound of computational complexity of knapsack problems
• Stochastic light in a cavity: A Brownian particle in a scalar potential?
• Minor embedding with Stuart-Landau oscillator networks
• Polaritonic Machine Learning for Graph-based Data Analysis
• Optical resonators constitute a universal spin simulator