Optical spin glasses

Abstract

Spin-glass theory emerged in the 1980s as a merger between theoretical physics and condensed matter. Soon, physicists realized that spin glasses serve as a paradigm for complex systems, as underscored by the 2021 Nobel Prize in Physics, and for applications in machine learning and neuroscience, with a profound connection with the Hopfield model and Boltzmann machines, subjects of the 2024 Nobel Prize in Physics. However, the connection with optics and photonics is even more profound and fundamental; this connection was identified as early as 1982, with the first realizations of optical neural networks. Thirty years later, the first experimental demonstration of a pillar of spin-glass theory, the replica symmetry breaking, was reported in photonics. Nowadays, many scientists consider photonics as an effective solution for new hardware in artificial intelligence, capable of reducing energy consumption in training large machine-learning modules, and also more suitable for realizing fully connected models that underpin modern data-driven analysis. The substantial equivalence between linear optical propagation and a system of interacting binary spins is now well recognized, triggering the development of a new family of devices for both classical and quantum computing. This review is intended to detail the work of the past twenty years concerning the link between spin-glass theory and optics. After a simple introduction to the main ideas of spin glasses, we start from the first works aimed at finding a direct experimental proof of ideas such as the landscape and ultrametricity; then we report on “linear optical spin glasses,” which refer to the photonic simulation of various Ising models for combinatorial optimization and interlinked with quantum computers; finally, we discuss the emerging field of “nonlinear optical spin glasses,” driven by the impressive progress in the realization of coherent Ising machines with parametric oscillators, that opened an new research direction driven by the cross-fertilization of advanced theoretical physics, artificial intelligence, classical and quantum nonlinear optics.