Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations

TL;DR

This paper introduces a neural differential equations approach for quantum Hamiltonian learning, enabling reliable inference of complex many-body dynamics and providing a new benchmark for evaluating such algorithms.

Contribution

The authors develop a novel neural differential equations method for Hamiltonian learning that is convergent, interpretable, and effective on previously unlearnable Hamiltonians.

Findings

Successfully infers quantum dynamics from state trajectories

Provides a new power-law based quantitative benchmark

Outperforms existing Hamiltonian learning algorithms on 1D spin chain

Abstract

Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under the action of such Hamiltonians. This inherent complexity limits our ability to characterise quantum many-body systems, highlighting the need for innovative approaches to unlock their full potential. To address this challenge, we propose a novel method to solve the Hamiltonian Learning (HL) problem-inferring quantum dynamics from many-body state trajectories-using Neural Differential Equations combined with an Ansatz Hamiltonian. Our method is reliably convergent, experimentally friendly, and interpretable, making it a stable solution for HL on a set of Hamiltonians previously unlearnable in the literature. In addition to this, we propose a new quantitative benchmark based on power laws, which can objectively compare the reliability and generalisation capabilities of any two HL algorithms. Finally, we benchmark our method against state-of-the-art HL algorithms with a 1D spin-1/2 chain proof of concept.