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arXiv:2404.05526 · Physical Review Applied

Hamiltonian learning using machine-learning models trained with continuous measurements

Kris Tucker, Amit Kiran Rege, Conor Smith, Claire Monteleoni, Tameem Albash

Published Oct 30, 2024• 5 citations
arXivHTMLPDF

Abstract

We build upon recent work on the use of machine-learning models to estimate Hamiltonian parameters using continuous weak measurement of qubits as input. We consider two settings for the training of our model: (1) supervised learning, where the weak-measurement training record can be labeled with known Hamiltonian parameters, and (2) unsupervised learning, where no labels are available. The first has the advantage of not requiring an explicit representation of the quantum state, thus potentially scaling very favorably to a larger number of qubits. The second requires the implementation of a physical model to map the Hamiltonian parameters to a measurement record, which we implement using an integrator of the physical model with a recurrent neural network to provide a model-free correction at every time step to account for small effects not captured by the physical model. We test our construction on a system of two qubits and demonstrate accurate prediction of multiple physical parameters in both the supervised context and the unsupervised context. We demonstrate that the model benefits from larger training sets, establishing that it is ``learning,'' and we show robustness regarding errors in the assumed physical model by achieving accurate parameter estimation in the presence of unanticipated single-particle relaxation.

DOI
10.1103/physrevapplied.22.044080

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Abstract Despite the complexity of quantum systems in the real world, models with just a few effective many-body states often suffice to describe their quantum dynamics, provided decoherence is accounted for. We show that a machine learning algorithm is able to construct such models, given a straightforward set of quantum dynamics measurements. The effective Hilbert space can be a black box, with variations of the coupling to just one accessible output state being sufficient to generate the required training data. We demonstrate through simulations of a Markovian open quantum system that a neural network can automatically detect the number N of effective states and the most relevant Hamiltonian terms and state-dephasing processes and rates. For systems with N ⩽ 5 we find typical mean relative errors of predictions in the 10 % range. With more advanced networks and larger training sets, it is conceivable that a future single software can provide the automated first stop solution to model building for an unknown device or system, complementing and validating the conventional approach based on physical insight into the system.
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We introduce a generalizable framework for identifying effective Hamiltonians directly from experimental data in solid-state quantum systems. Our unsupervised autoencoder-based approach incorporates the governing physics (here, the S-matrix formalism) directly into the decoder, enabling physically meaningful Hamiltonian inference without labeled Hamiltonian parameters. Through numerical experiments on a triple quantum dot chain, we demonstrate automated characterization of programmable solid-state simulators from transport measurements. The model accurately infers Hamiltonian parameters and generalizes beyond the training domain, while exhibiting finite capacity as the parameter space becomes increasingly broad or diverse. We further demonstrate robustness to noisy measurements and show that the model can be trained on transport data generated outside the Hamiltonian family assumed by the physics decoder, while still identifying meaningful effective parameters.