Hamiltonian Learning at Heisenberg Limit for Hybrid Quantum Systems

TL;DR

This paper introduces a theoretically rigorous, Heisenberg-limited algorithm for estimating unknown spin-boson Hamiltonian parameters in hybrid quantum systems, achieving high precision with minimal measurements and robustness to errors.

Contribution

The work presents a novel, scalable algorithm for Hamiltonian learning at the Heisenberg limit, including an alternative distributed sensing approach that reduces evolution time.

Findings

Achieves Heisenberg-limited estimation with O(ε^{-1}) time

Requires only polylogarithmic measurements in precision

Demonstrates efficiency in hybrid Hamiltonian and spectrum learning

Abstract

Hybrid quantum systems with different particle species are fundamental in quantum materials and quantum information science. In this work, we establish a rigorous theoretical framework proving that, given access to an unknown spin-boson type Hamiltonian, our algorithm achieves Heisenberg-limited estimation for all coupling parameters up to error $\epsilon$ with a total evolution time ${O}(\epsilon^{-1})$ using only ${O}({\rm polylog}(\epsilon^{-1}))$ measurements. It is also robust against small state preparation and measurement errors. In addition, we provide an alternative algorithm based on distributed quantum sensing, which significantly reduces the evolution time per measurement. To validate our method, we demonstrate its efficiency in hybrid Hamiltonian learning and spectrum learning, with broad applications in AMO, condensed matter and high energy physics. Our results provide a scalable and robust framework for precision Hamiltonian characterization in hybrid quantum platforms.