Continuous-time parametrization of neural quantum states for quantum dynamics

TL;DR

This paper introduces a continuous-time neural quantum state framework that improves quantum dynamics simulation accuracy and efficiency by using a differentiable, basis-function parameterization of neural network parameters.

Contribution

It proposes a novel smooth neural quantum state (s-NQS) approach with a continuous, differentiable parameterization for better quantum dynamics modeling.

Findings

Accurate time evolution with fewer parameters.

Ability to evaluate wave function at arbitrary times.

Effective for non-integrable quantum spin chains.

Abstract

Neural quantum states are a promising framework for simulating many-body quantum dynamics, as they can represent states with volume-law entanglement. As time evolves, the neural network parameters are typically optimized at discrete time steps to approximate the wave function at each point in time. Given the differentiability of the wave function stemming from the Schr\"odinger equation, here we impose a time-continuous and differentiable parameterization of the neural network by expressing its parameters as linear combinations of temporal basis functions with trainable, time-independent coefficients. We test this ansatz, referred to as the smooth neural quantum state (\textit{s}-NQS) with a loss function defined over an extended time interval, under a sudden quench of a non-integrable many-body quantum spin chain. We demonstrate accurate time evolution using a restricted Boltzmann machine as the instantaneous neural network architecture. We show that the parameterization enables accurate simulations with fewer variational parameters, independent of time-step resolution. Furthermore, the smooth neural quantum state also allows us to initialize and evaluate the wave function at times not included in the training set, both within and beyond the training interval.