  Neural quantum states (NQSs) have emerged as a novel promising numerical
method to solve the quantum many-body problem. However, it has remained a
central challenge to train modern large-scale deep network architectures to
desired quantum state accuracy, which would be vital in utilizing the full
power of NQSs and making them competitive or superior to conventional numerical
approaches. Here, we propose a minimum-step stochastic reconfiguration (MinSR)
method that reduces the optimization complexity by orders of magnitude while
keeping similar accuracy as compared to conventional stochastic
reconfiguration. MinSR allows for accurate training on unprecedentedly deep NQS
with up to 64 layers and more than $10^5$ parameters in the spin-1/2 Heisenberg
$J_1$-$J_2$ models on the square lattice. We find that this approach yields
better variational energies as compared to existing numerical results and we
further observe that the accuracy of our ground state calculations approaches
different levels of machine precision on modern GPU and TPU hardware. The MinSR
method opens up the potential to make NQS superior as compared to conventional
computational methods with the capability to address yet inaccessible regimes
for two-dimensional quantum matter in the future.
