Simulation of Hopfield-like Hamiltonians using time-multiplexed photonic networks

TL;DR

This paper introduces a photonic network architecture that uses time-multiplexed resonators to simulate complex Hamiltonian dynamics, including models like Hopfield and Tavis-Cummings, enabling scalable optical quantum simulations.

Contribution

It presents a novel photonic network design capable of emulating Hamiltonian dynamics, including nonlinear and many-body phenomena, advancing optical quantum simulation capabilities.

Findings

Successfully reproduces Hopfield model dynamics in a photonic setup.

Proposes a scalable method for simulating nonlinear light-matter interactions.

Establishes a versatile framework for simulating collective quantum phenomena.

Abstract

We propose a time-multiplexed photonic network architecture based on coupled ring resonators, capable of accurately emulating specific Hamiltonian dynamics. We show that, in the Suzuki-Trotter limit, the resulting stroboscopic evolution reproduces the characteristic dynamics of the bosonized Hopfield model. Furthermore, by incorporating a nonlinear element within the main resonator loop, we outline a scalable route toward optical simulation of both mean-field and quantum nonlinear dynamics associated with the Tavis-Cummings model. Our results establish time-multiplexed resonator networks as a versatile photonic framework for simulating interacting light-matter Hamiltonians and collective many-body phenomena.