Optical computation of a spin glass dynamics with tunable complexity
Marco Leonetti, Erik Hormann, Luca Leuzzi, Giorgio Parisi, Giancarlo Ruocco
Abstract
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 [Formula: see text] 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 [Formula: see text] We study experimentally, numerically, and analytically this Hopfield-like system displaying a paramagnetic, ferromagnetic, and SG phase, and we demonstrate that the transition temperature [Formula: see text] to the glassy phase from the paramagnetic phase grows with α. 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.