Optical computation of a spin glass dynamics with tunable complexity

Spin glasses (SGs) are paradigmatic models for physical, computer science, biological, and social systems. The problem of studying the dynamics for SG models is nondetermistic polynomial-time (NP) hard; that is, no algorithm solves it in polynomial time. Here we implement the optical simulation of an SG, exploiting the N segments of a wavefront-shaping device to play the role of the spin variables, combining the interference 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 are user defined, acting on the ratio P/N = alpha. We study experimentally, numerically, and analytically this Hopfield-like system displaying a paramagnetic, ferromagnetic, and SG phase, and we demonstrate that the transition temperature T-g to the glassy phase from the paramagnetic phase grows with alpha. We demonstrate the computational advantage of the optical SG where interaction terms are realized simultaneously when the independent light rays interfere on the detector's surface. This inherently parallel measurement of the energy provides a speedup with respect to purely in silico simulations scaling with N.

Automated summary

Studying the dynamics of spin glass models is a complex and nondeterministic problem. Researchers have implemented optical simulation to study the spin glass system and demonstrate transitions between different phases. Optical SG offers computational advantages with parallel measurements, leading to speedup in calculations.