Computing the ground state of interacting quantum matter, especially for complex two-dimensional systems, is a long-standing challenge. Neural quantum states (NQSs), encoding many-body wavefunctions into artificial neural networks, offer potential. However, existing optimization algorithms are unsuitable for large-scale deep network architectures. This paper introduces a minimum-step stochastic-reconfiguration (MinSR) optimization algorithm, enabling training of deep NQSs with up to 10⁶ parameters. Applied to frustrated spin-1/2 models, MinSR achieves machine precision, yielding improved variational energies and providing numerical evidence for gapless quantum-spin-liquid phases.

Ao Chen, Markus Heyl