  Neural quantum states have established themselves as a powerful and versatile
family of ansatzes for variational Monte Carlo simulations of quantum many-body
systems. Of particular prominence are autoregressive neural quantum states
(ANQS), which enjoy the expressibility of deep neural networks, and are
equipped with a procedure for fast and unbiased sampling. Yet, the
non-selective nature of autoregressive sampling makes incorporating quantum
number symmetries challenging. In this work, we develop a general framework to
make the autoregressive sampling compliant with an arbitrary number of quantum
number symmetries. We showcase its advantages by running electronic structure
calculations for a range of molecules with multiple symmetries of this kind. We
reach the level of accuracy reported in previous works with more than an order
of magnitude speedup and achieve chemical accuracy for all studied molecules,
which is a milestone unreported so far. Combined with the existing effort to
incorporate space symmetries, our approach expands the symmetry toolbox
essential for any variational ansatz and brings the ANQS closer to being a
competitive choice for studying challenging quantum many-body systems.
