Scaling of the tVMC Time Step with System Size

Determine how the stable integration time step size used in time-dependent variational Monte Carlo scales with the system size for ab initio electronic systems, taking into account the computational costs associated with evaluating local energies, computing parameter gradients, and inverting the quantum geometric tensor.

Background

The scalability of time-dependent variational Monte Carlo (tVMC) depends on multiple factors: evaluating the local energy (dominated by Laplacians) scales as O(N^4) with the number of electrons N, and solving the time-dependent variational principle requires inverting the quantum geometric tensor, which scales as O(N_p^3) with the number of variational parameters N_p.

While these costs are analyzed, the dependence of the permissible time step on system size remains unspecified. Clarifying this scaling is important for predicting runtime and stability of real-time simulations as system size grows.