Adaptive quantum dynamics with the time-dependent variational Monte Carlo method

TL;DR

This paper presents an adaptive extension to the time-dependent variational Monte Carlo method that selectively updates the most relevant parameters, improving stability and accuracy in simulating quantum dynamics with complex wave functions.

Contribution

The paper introduces an adaptive tVMC method that uses relevance estimates to control variational expressivity, enhancing stability and efficiency in quantum dynamics simulations.

Findings

Improved numerical stability in quantum dynamics simulations.

Reduced regularization needs with highly expressive ans"atze.

Effective benchmarking on the transverse-field Ising model.

Abstract

We introduce an extension of the time-dependent variational Monte Carlo (tVMC) method that adaptively controls the expressivity of the variational quantum state during the simulation of the dynamics. This adaptive tVMC (atVMC) approach is specifically designed to enhance numerical stability when overparameterized variational ans\"atze lead to ill-conditioned equations of motion. Building on the concept of the local-in-time error (LITE), a measure of the deviation between variational and exact evolution, we introduce a procedure to quantify each parameter's contribution to reducing the LITE, using only quantities already computed in standard tVMC simulations. These relevance estimates guide the selective evolution of only the most significant parameters at each time step, while maintaining a prescribed level of accuracy. We benchmark the algorithm on quantum quenches in the one-dimensional transverse-field Ising model using both spin-Jastrow and restricted Boltzmann machine wave functions, with an emphasis on overparameterized regimes. The adaptive scheme significantly improves numerical stability and reduces the need for strong regularization, enabling reliable simulations with highly expressive variational ans\"atze.