Benchmarking discrete truncated Wigner approximation and neural network quantum states with the exact dynamics in a Rydberg atomic chain

TL;DR

This paper compares the effectiveness of the discrete truncated Wigner approximation and neural quantum states in modeling excitation and correlation dynamics in a Rydberg atomic chain, highlighting the strengths and limitations of each method.

Contribution

It provides a systematic benchmarking of DTWA and NQS against exact dynamics in a Rydberg chain, revealing NQS's superior performance in certain quantum correlation calculations.

Findings

NQS accurately predicts time-averaged excitations across interaction strengths.

DTWA diverges from exact results at high Rydberg interactions.

NQS shows promise in calculating quantum correlations like Rènyi entropies.

Abstract

We benchmark the discrete truncated Wigner approximation (DTWA) and Neural quantum states (NQS) based on restricted Boltzmann-like machines with the exact excitation and correlation dynamics in a chain of ten Rydberg atoms. The initial state is where all atoms are in their electronic ground state. We characterize the excitation dynamics using the maximum and time-averaged number of Rydberg excitations. DTWA results are different from the exact dynamics for large Rydberg-Rydberg interactions. In contrast, by increasing the number of hidden spins, the NQS can be improved but still limited to short-time dynamics. Interestingly, irrespective of interaction strengths, the time-averaged number of excitations obtained using NQS is in excellent agreement with the exact results. Concerning the calculation of quantum correlations, for instance, second-order bipartite and average two-site R\'enyi entropies, NQS looks more promising. Finally, we discuss the existence of a power law scaling for the initial growth of average two-site R\'enyi entropy.