Multiphoton Quantum Simulation of the Generalized Hopfield Memory Model

In the present Letter, we introduce, develop, and investigate a connection between multiphoton quantum interference, a core element of emerging photonic quantum technologies, and Hopfield-like Hamiltonians of classical neural networks, the paradigmatic models for associative memory and machine learning in systems of artificial intelligence. Specifically, we show that combining a system composed of N_{ph} indistinguishable photons in superposition over M field modes, a controlled array of M binary phase shifters, and a linear-optical interferometer, yields output photon statistics described by means of a p-body Hopfield Hamiltonian of M Ising-like neurons ±1, with p=2N_{ph}. We investigate in detail the generalized four-body Hopfield model obtained through this procedure, undergoing a transition from a memory retrieval to a memory black-out regime, i.e., a spin-glass phase, as the amount of stored memory increases. The mapping enables novel routes to the realization and investigation of disordered and complex classical systems via efficient photonic quantum simulators and describes aspects of structured photonic systems in terms of classical spin Hamiltonians.