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arXiv:2205.11977 · Annual Reviews in Control

Parameter estimation and system identification for continuously-observed quantum systems

Hendra I. Nurdin, Mădălin Guţǎ

Published Jan 1, 2022• 28 citations
arXivHTMLPDF
DOI
10.1016/j.arcontrol.2022.04.012

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An observer-based Hamiltonian identification algorithm for quantum systems has been recently proposed by two of the authors to estimate the dipole moment matrix of a quantum system requiring the measurement of the populations on all states. This could be experimentally difficult to achieve. We propose here an extension to a 3-level quantum system, having access to the population of the ground state only. By a suitable choice of the control field, we show that a continuous measurement of this population, alone, is enough to identify the field coupling parameters (dipole moment). Simulations with 20% of noise on the measured population illustrate the robustness of the proposed estimation algorithm and confirm the convergence analysis.
Estimating the parameters that dictate the dynamics of a quantum system is an important task for quantum information processing and quantum metrology, as well as fundamental physics. In this paper we develop a method for parameter estimation for Markovian open quantum systems using a temporal record of measurements on the system. The method is based on system realization theory and is a generalization of our previous work on identification of Hamiltonian parameters [Phys. Rev. Lett. 113, 080401 (2014)].
This technical note studies the identification of unknown decoherence rates for a class of two-level quantum systems undergoing spontaneous emission. Our previous work shows that estimates of the unknown decoherence rates can be obtained from the ensemble averages by imposing constant control and monitoring a sequence of identical systems continuously. Inspired by the work, this technical note further investigates the identification based on a single quantum system. It is shown that a mean-ergodic solution exists for a single system under constant control and convergence to an ergodic process can be guaranteed by introducing some noise into the control signals. The ensemble average can thus be replaced by the time average of a single system, and the parameter estimate can be obtained from a single implementation.
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