Variational Excited-State Algorithms with Neural Quantum States

Artificial neural networks have proven to be flexible and effective tools for representing ground-state wave functions, particularly in strongly interacting fermionic systems. In this work, we extend variational neural quantum state (NQS) methods to target low-lying excited states by constructing an orthogonal subspace that evolves jointly through imaginary-time propagation. The algorithm combines reinforcement and supervised learning techniques, and requires only minimal symmetry and boundary condition constraints, making it broadly applicable across many-body systems, including finite nuclei. We benchmark the method on testbed problems and discuss its potential for studying excitation spectra and correlation structure in nuclear systems.