Robust Online Hamiltonian Learning

Abstract

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.

24 pages, 12 figures; to appear in New Journal of Physics

References in corpus (9)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Direct Fidelity Estimation from Few Pauli Measurements
• Quantum simulation of the Klein paradox with trapped ions
• Time-Symmetric Quantum Theory of Smoothing
• Nanoscale magnetometry using a single spin system in diamond
• Robust error bars for quantum tomography
• Equation of motion for process matrix: Hamiltonian identification and dynamical control of open quantum systems
• Accurate quantum state estimation via "Keeping the experimentalist honest"
• Optimizing qubit Hamiltonian parameter estimation algorithms using PSO

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• Accelerated Randomized Benchmarking
• Machine learning \& artificial intelligence in the quantum domain
• Quantum Bootstrapping via Compressed Quantum Hamiltonian Learning
• Experimental adaptive process tomography
• Adaptive quantum tomography
• Quantum Model Averaging
• Statistical Inference with Quantum Measurements: Methodologies for Nitrogen Vacancy Centers in Diamond
• The best Fisher is upstream: data processing inequalities for quantum metrology
• Simultaneous model selection and parameter estimation: A superconducting qubit coupled to a bath of incoherent two-level systems