Continuous-variable neural network quantum states and the quantum rotor model

We initiate the study of neural network quantum state algorithms for analyzing continuous-variable quantum systems in which the quantum degrees of freedom correspond to coordinates on a smooth manifold. A simple family of continuous-variable trial wavefunctions is introduced which naturally generalizes the restricted Boltzmann machine (RBM) wavefunction introduced for analyzing quantum spin systems. By virtue of its simplicity, the same variational Monte Carlo training algorithms that have been developed for ground state determination and time evolution of spin systems have natural analogues in the continuum. We offer a proof of principle demonstration in the context of ground state determination of a stoquastic quantum rotor Hamiltonian. Results are compared against those obtained from partial differential equation (PDE) based scalable eigensolvers. This study serves as a benchmark against which future investigation of continuous-variable neural quantum states can be compared, and points to the need to consider deep network architectures and more sophisticated training algorithms.

Automated summary

We introduce the exploration of neural network quantum state algorithms for analyzing continuous-variable quantum systems. A simple family of continuous-variable trial wavefunctions is proposed, which generalizes the restricted Boltzmann machine (RBM) wavefunction for analyzing quantum spin systems. The same variational Monte Carlo training algorithms for spin systems have natural analogues in the continuum. We demonstrate the feasibility for ground state determination of a stoquastic quantum rotor Hamiltonian and compare the results with PDE-based scalable eigensolvers. This study provides a benchmark for future investigation of continuous-variable neural quantum states and highlights the need for deep network architectures and more sophisticated training algorithms.