Continuous-variable neural-network quantum states and the quantum rotor model
This work provides a benchmark for future research in continuous-variable neural quantum states, but it is incremental as it adapts existing methods to a new domain.
The authors tackled the problem of analyzing continuous-variable lattice quantum systems by introducing a neural-network quantum state algorithm that generalizes restricted Boltzmann machines to continuous variables, demonstrating it on a quantum rotor model and comparing results against PDE-based eigensolvers.
We initiate the study of neural-network quantum state algorithms for analyzing continuous-variable lattice quantum systems in first quantization. A simple family of continuous-variable trial wavefunctons 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.