Optical computation of a spin glass dynamics with tunable complexity

TL;DR

This paper demonstrates an optical simulation of spin glass dynamics using wavefront shaping, enabling parallel energy measurements and exploring phase transitions with tunable complexity, offering a novel approach to studying complex systems.

Contribution

It introduces an optical method to simulate spin glass dynamics, leveraging interference and wavefront shaping for parallel energy computation, which is faster and more scalable than traditional digital simulations.

Findings

Successfully simulated spin glass phases including paramagnetic, ferromagnetic, and glassy.

Showed the transition temperature to the glassy phase increases with the complexity parameter.

Demonstrated the method's ability to explore complex energy landscapes efficiently.

Abstract

Spin Glasses (SG) are paradigmatic models for physical, computer science, biological and social systems. The problem of studying the dynamics for SG models is NP hard, i.e., no algorithm solves it in polynomial time. Here we implement the optical simulation of a SG, exploiting the N segments of a wavefront shaping device to play the role of the spin variables, combining the interference at downstream of a scattering material to implement the random couplings between the spins (the J ij matrix) and measuring the light intensity on a number P of targets to retrieve the energy of the system. By implementing a plain Metropolis algorithm, we are able to simulate the spin model dynamics, while the degree of complexity of the potential energy landscape and the region of phase diagram explored is user-defined acting on the ratio the P/N = \alpha. We study experimentally, numerically and analytically this peculiar system displaying a paramagnetic, a ferromagnetic and a SG phase, and we demonstrate that the transition temperature T g to the glassy phase from the paramagnetic phase grows with \alpha. With respect to standard in silico approach, in the optical SG interaction terms are realized simultaneously when the independent light rays interferes at the target screen, enabling inherently parallel measurements of the energy, rather than computations scaling with N as in purely in silico simulations.