Expressive power of complex-valued restricted Boltzmann machines for solving nonstoquastic Hamiltonians

Variational Monte Carlo with neural quantum states is one of the most powerful tools for solving the ground state of quantum many-body Hamiltonians. However, the performance of the method on frustrated Hamiltonians remains significantly worse than that of sign-free Hamiltonians, even though the method itself is free from sum-over alternating signs. Here, the authors systematically study numerical subtleties in restricted Boltzmann machine based variational Monte Carlo for solving Hamiltonians with the sign problem and unveil how quantum phases are related to the numerics.