Maximum-Likelihood-Estimate Hamiltonian learning via efficient and robust quantum likelihood gradient

TL;DR

This paper introduces an efficient maximum likelihood-based method for learning Hamiltonians in quantum many-body systems, combining gradient descent with quantum algorithms to improve accuracy, stability, and scalability.

Contribution

It presents a novel Hamiltonian learning approach that leverages quantum likelihood gradients, ensuring efficiency, locality preservation, and robustness against noise and fluctuations.

Findings

Outperforms previous methods in accuracy and stability

Extends to larger systems using quantum many-body algorithms

Demonstrates robustness to noise, fluctuations, and temperature variations

Abstract

Given the recent developments in quantum techniques, modeling the physical Hamiltonian of a target quantum many-body system is becoming an increasingly practical and vital research direction. Here, we propose an efficient strategy combining maximum likelihood estimation, gradient descent, and quantum many-body algorithms. Given the measurement outcomes, we optimize the target model Hamiltonian and density operator via a series of descents along the quantum likelihood gradient, which we prove is negative semi-definite with respect to the negative-log-likelihood function. In addition to such optimization efficiency, our maximum-likelihood-estimate Hamiltonian learning respects the locality of a given quantum system, therefore, extends readily to larger systems with available quantum many-body algorithms. Compared with previous approaches, it also exhibits better accuracy and overall stability toward noises, fluctuations, and temperature ranges, which we demonstrate with various examples.