Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm

TL;DR

This paper demonstrates that the ESPRIT algorithm can effectively extrapolate long-time quantum system dynamics from short-time data, providing a noise-robust, data-driven method for predicting quantum behavior without relying on physical models.

Contribution

The work applies ESPRIT to quantum dynamics, showing its ability to accurately predict long-time behavior from limited short-time data, a novel use in quantum simulations.

Findings

ESPRIT accurately predicts long-time quantum dynamics from short-time data.

The method is robust to noise in the data.

ESPRIT can determine the minimal data length needed for reliable extrapolation.

Abstract

Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases.