Emergent Equilibrium in All-Optical Single Quantum-Trajectory Ising Machines

TL;DR

This paper demonstrates that multi-mode all-optical quantum systems can emulate thermal equilibrium states described by an Ising Hamiltonian, enabling ultra-fast Boltzmann sampling for optimization tasks.

Contribution

It reveals how dissipative coupling in driven optical systems leads to emergent thermal equilibrium governed by an Ising model, with potential for rapid optimization hardware.

Findings

Single Gaussian quantum trajectories show emergent thermal equilibrium.

Effective temperature controlled by driving strength.

Potential for ultra-fast Boltzmann sampling in optical devices.

Abstract

We investigate the dynamics of multi-mode optical systems driven by two-photon processes and subject to non-local losses, incorporating quantum noise at the Gaussian level. Our findings show that the statistics retrieved from a single Gaussian quantum trajectory exhibits emergent thermal equilibrium governed by an Ising Hamiltonian, encoded in the dissipative coupling between modes. The system's effective temperature is set by the driving strength relative to the oscillation threshold. Given the ultra-short time scales typical of all-optical devices, our study demonstrates that such multi-mode optical systems can operate as ultra-fast Boltzmann samplers, paving the way towards the realization of efficient hardware for combinatorial optimization, with promising applications in machine learning and beyond.