High-accuracy Hamiltonian learning via delocalized quantum state evolutions

TL;DR

This paper introduces a Hamiltonian learning method using repeated measurements on delocalized quantum states, demonstrating that delocalization enhances learning accuracy and providing error analysis and simulation examples.

Contribution

It establishes delocalization as a quantum resource for Hamiltonian learning and proposes an optimal state preparation strategy for improved accuracy.

Findings

Delocalized states maximize Hamiltonian learning accuracy.

Error scales favorably with the number of measurements.

Simulations validate the proposed learning algorithm.

Abstract

Learning the unknown Hamiltonian governing the dynamics of a quantum many-body system is a challenging task. In this manuscript, we propose a possible strategy based on repeated measurements on a single time-dependent state. We prove that the accuracy of the learning process is maximized for states that are delocalized in the Hamiltonian eigenbasis. This implies that delocalization is a quantum resource for Hamiltonian learning, that can be exploited to select optimal initial states for learning algorithms. We investigate the error scaling of our reconstruction with respect to the number of measurements, and we provide examples of our learning algorithm on simulated quantum systems.