Enhancing Variational Monte Carlo with Neural Network Quantum States*

Rydberg atom arrays are promising candidates for high-quality quantum computation and quantum simulation. However, long state preparation times limit the amount of measurement data that can be generated at reasonable timescales. This restriction directly affects the estimation of operator expectation values, as well as the reconstruction and characterization of quantum states.

Over the last years, neural networks have been explored as a powerful and systematically tuneable ansatz to represent quantum wave functions. Via tomographical state reconstruction, such numerical models can significantly reduce the amount of necessary measurements to accurately reconstruct operator expectation values. At the same time, neural networks can find ground state wave functions of given Hamiltonians via variational energy minimization.

In this talk, I apply both the data-driven and Hamiltonian-driven training procedures to reconstruct the ground state of a two-dimensional array of Rydberg atoms in the vicinity of a quantum phase transition. I demonstrate the limitations of the individual approaches and introduce methods to advance the performance of the network model. I further investigate and interpret significant behaviors in the network training process. Combining data-driven and Hamiltonian-driven network training, I show that the variational ground state search can be significantly enhanced by naturally finding an improved network initialization from a limited amount of measurement data.