Learning Quantum Operator Dynamics from Short-Time Data

TL;DR

This paper introduces a neural ODE-based method that reconstructs long-time quantum operator dynamics from short-time data, enabling spectral analysis and excitation spectrum resolution in noisy quantum systems.

Contribution

It presents a physics-informed neural ODE framework that leverages locality and symmetry to efficiently extrapolate quantum dynamics from limited short-time measurements.

Findings

Accurately predicts long-time behavior of quantum observables.

Resolves excitation spectra from noisy short-time data.

Demonstrates scalability and data efficiency on quantum hardware.

Abstract

Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence. We propose a neural ordinary differential equation (Neural ODE) framework with physics-driven designs to reconstruct long-time operator dynamics from short-time measurements. By expanding observables in the Pauli basis and exploiting locality and symmetry constraints, the operator evolution is reduced to a tractable set of coefficients whose dynamics are learned from data. Applied to the transverse-field Ising model, the method accurately extrapolates long-time behavior and resolves excitation spectra from noisy short-time signals. Our results demonstrate a scalable and data-efficient strategy for extracting dynamical and spectral information from practical quantum hardware.