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 (27)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Universal digital quantum simulation with trapped ions
• Direct Fidelity Estimation from Few Pauli Measurements
• Simulation-based optimal Bayesian experimental design for nonlinear systems
• Practical characterization of quantum devices without tomography
• Quantum simulation of the Klein paradox with trapped ions
• Machine Learning for Precise Quantum Measurement
• Quantum Process Tomography of the Quantum Fourier Transform
• Adaptive Bayesian Quantum Tomography
• Time-Symmetric Quantum Theory of Smoothing
• An Efficient Algorithm for Optimizing Adaptive Quantum Metrology Processes
• Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing
• A Robust Method for Estimating the Lindblad Operators of a Dissipative Quantum Process from Measurements of the Density Operator at Multiple Time Points
• Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis
• How to best sample a periodic probability distribution, or on the accuracy of Hamiltonian finding strategies
• Bayesian Adaptive Exploration
• Nanoscale magnetometry using a single spin system in diamond
• Separable Measurement Estimation of Density Matrices and its Fidelity Gap with Collective Protocols
• Selective and Efficient Quantum Process Tomography
• Incoherent Noise and Quantum Information Processing
• Simplified Quantum Process Tomography
• Robust error bars for quantum tomography
• Equation of motion for process matrix: Hamiltonian identification and dynamical control of open quantum systems
• Adaptive Hamiltonian Estimation Using Bayesian Experimental Design
• Accurate quantum state estimation via "Keeping the experimentalist honest"
• Optimizing qubit Hamiltonian parameter estimation algorithms using PSO

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