Learning Quantum Phases of Matter Using a Basis-Enhanced Born Machine*

The interplay between charge, spin, and other degrees of freedom in a quantum system is responsible for the emergence of exotic quantum phases, which range from ferromagnetic to spin liquid. The generative Born Machine is a quantum inspired machine learning tool that aims to learn a joint probability distribution from classical or quantum data obtained from simulation or experiment.  However, the full potential of the Born Machine in learning from quantum data has thus far been unrealized. In this work, by assembling training data from two distinct bases, we create a basis-enhanced Born Machine that is well-suited for pure quantum state reconstruction. We use the basis-enhanced Born Machine to learn across the ground state phase diagram of a 1D chain of Rydberg atoms and that of a 1D XY spin chain, accurately predicting quantum correlations and other observables. It is demonstrated that the improved model is able to capture the quantum state in various ordered phases as well as at the critical point to a quantum fidelity as high as 99%.