Learning Energy-Based Representations of Many-Body Quantum States

We propose a new generative classical representation of many-body quantum states. This energy-based representation is derived from Gibbs distributions used for modeling thermal states of classical spin systems. This approach has the advantage of focusing on the structure of the energy function instead of attempting to directly model the probability density function. Based on the prior information on a family of quantum states, the energy function can be parametrized by an explicit low-degree polynomial or by a generic parametric family such as neural nets, and can naturally include the known symmetries of the system. In this work, we show how to efficiently learn the energy function representations for different families of quantum states from the available measurement data. Through a variety of examples, we show that the learned models can be used as generative models for predicting expectation values of physical observables.