  Combining insights from machine learning and quantum Monte Carlo, the
stochastic reconfiguration method with neural network Ansatz states is a
promising new direction for high-precision ground state estimation of quantum
many-body problems. Even though this method works well in practice, little is
known about the learning dynamics. In this paper, we bring to light several
hidden details of the algorithm by analyzing the learning landscape. In
particular, the spectrum of the quantum Fisher matrix of complex restricted
Boltzmann machine states exhibits a universal initial dynamics, but the
converged spectrum can dramatically change across a phase transition. In
contrast to the spectral properties of the quantum Fisher matrix, the actual
weights of the network at convergence do not reveal much information about the
system or the dynamics. Furthermore, we identify a new measure of correlation
in the state by analyzing entanglement in eigenvectors. We show that,
generically, the learning landscape modes with least entanglement have largest
eigenvalue, suggesting that correlations are encoded in large flat valleys of
the learning landscape, favoring stable representations of the ground state.

Quantum Physics;Statistical Mechanics;Machine Learning