Boltzmann machines as thermal models for quantum systems

Abstract

We successfully model the behavior of two-spin systems using neural networks known as conditional Restricted Boltzmann Machines (cRBMs) which encode physical information in the properties of a thermal ensemble akin to an Ising model. The result gives local "hidden" variable models for product states and entangled states, including the singlet state used in the EPR-Bohm experiment. Bell's theorem is circumvented because the state of the system is dependent not only on the preparation but also on the measurement setup (the detector settings). Though at first glance counterintuitive, the apparent "retrocausality" in these models has a historical precedent in the absorber theory of Wheeler and Feynman and an intuitive analog in the simple AC circuit of an electric guitar.