Applying Neural Quantum States to Real-Time Electronic Dynamics
Develop and validate a framework that applies Neural Quantum States to accurately model the real-time quantum dynamics of interacting electronic systems in continuous space by extending variational Monte Carlo to time-dependent evolution, thereby enabling correlated, beyond-mean-field simulations of the time-dependent Schrödinger equation for ab initio electronic structure problems.
References
NQS promise to provide high-accuracy wave functions, capturing the entire entanglement of the system, at an affordable computational cost. However, their application to study quantum dynamics, where correlations are expected to be essential, remains an open problem.
Three extensions follow naturally from this work. First, we can create versions of Hamilton-zero that were fine-tuned on larger datasets to boost its performance in sector-specific problem families such as quantum chemistry or combinatorial optimisation. This would likely further amortize subsequent fine-tuning of individual systems and lead to even stronger zero-shot inference. Second, we can extend Hamilton-Zero's capabilities from static ground state problems to dynamics via a time encoding. For a pretraining dataset of time-dependent Hamiltonians $H(t)$, we could train against the Schr"odinger residual $i\partial_t\psi_\theta-H(t)\psi_\theta$ together with an initial-condition loss, as was done in deep stochastic mechanics of bosonic systems \citep{orlova2023deep}. Finally, a per-site-odd but nonlinear successor could use higher half-integer Peter--Weyl sectors. Unlike the multilinear architecture used here, it would require the certified Casimir penalty of Appendix~\ref{app:casimir-reg} to retain a physical upper bound. We leave both constructions and their validation to future work.