Hamiltonian Learning at Heisenberg Limit for Hybrid Quantum Systems

2025-02-27

AI Summary

This work addresses Hamiltonian learning in hybrid spin-boson systems, aiming to estimate coupling parameters at the Heisenberg limit while remaining robust against state preparation and measurement (SPAM) errors. Methodologically, we develop the first rigorously proven Heisenberg-limited framework for hybrid quantum systems—achieving estimation error $varepsilon$ with total evolution time $T = O(varepsilon^{-1})$ and logarithmic measurement overhead—and design a SPAM-robust algorithm along with a distributed quantum sensing variant that drastically reduces the maximal single-shot evolution time. Leveraging tools from quantum parameter estimation, adaptive measurement strategies, and rigorous error analysis, our approach enables high-precision Hamiltonian characterization in the generalized Dicke model and efficient spectral learning in spin-boson models. Numerical and analytical validation confirms scalability and robustness on realistic hybrid quantum platforms.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Hybrid quantum systems with different particle species are fundamental in quantum materials and quantum information science. In this work, we demonstrate that Hamiltonian learning in hybrid spin-boson systems can achieve the Heisenberg limit. Specifically, we establish a rigorous theoretical framework proving that, given access to an unknown hybrid Hamiltonian system, our algorithm can estimate the Hamiltonian coupling parameters up to root mean square error (RMSE) $epsilon$ with a total evolution time scaling as $T sim mathcal{O}(epsilon^{-1})$ using only $mathcal{O}({ m polylog}(epsilon^{-1}))$ measurements. Furthermore, it remains robust against small state preparation and measurement (SPAM) errors. In addition, we also provide an alternative algorithm based on distributed quantum sensing, which significantly reduces the maximum evolution time per measurement. To validate our method, we apply it to the generalized Dicke model for Hamiltonian learning and the spin-boson model for spectrum learning, demonstrating its efficiency in practical quantum systems. These results provide a scalable and robust framework for precision quantum sensing and Hamiltonian characterization in hybrid quantum platforms.

Problem

• Achieving Heisenberg limit in Hamiltonian learning for hybrid quantum systems.
• Estimating Hamiltonian coupling parameters with minimal measurements and robust against errors.
• Providing scalable framework for precision quantum sensing in hybrid platforms.

Innovation

• Achieves Heisenberg limit in Hamiltonian learning
• Uses polylogarithmic measurements for error scaling
• Robust against state preparation and measurement errors