Quantum System Identification by Bayesian Analysis of Noisy Data: Beyond Hamiltonian Tomography

Abstract

We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy data. Here we show how to generalize this approach to systems with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the process for a range of three-level quantum systems. The results suggest that the Bayesian estimation of the frequencies and dephasing rates is generally highly accurate and the main source of errors are errors in the reconstructed Hamiltonian basis.

6 pages, 3 figures

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• The ubiquitous problem of learning system parameters for dissipative two-level quantum systems: Fourier analysis versus Bayesian estimation
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• Model discrimination for dephasing two-level systems
• Assessing thermalization and estimating the Hamiltonian with output data only