Boltzmann machines as thermal models for quantum systems

Understand

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.