Practical Black Box Hamiltonian Learning

TL;DR

This paper introduces an improved protocol for learning quantum Hamiltonian parameters efficiently, with better scaling and precise hyperparameter tuning, demonstrated through simulations on an 80-qubit system.

Contribution

It presents a novel Hamiltonian learning protocol that enhances scalability and provides exact bounds for optimal hyperparameter settings.

Findings

Improved scaling with respect to Hamiltonian structure parameters.

Derived exact bounds for hyperparameter optimization.

Successful simulation on an 80-qubit system.

Abstract

We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality $k$). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol is practical for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.