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Mediterranean Conference on Control and Automation (MED)

On-Line State Estimation of 2-qubit Quantum Systems

Yaru Tang, Shuang Cong

Published Jul 1, 2019• 0 citations
Publisher

Abstract

In this paper, the online estimation of 2-qubit states is studied based on the quantum continuous weak measurement and compressed sensing (CS) theory. The stochastic master equation is used to describe the dynamic evolution of the system. The weak measurement operator acting on the system and the dynamic equation of the measurement operator over time are derived. The number of measurements is reduced based on the CS theory. The non-negative LS algorithm is used to reconstruct the quantum system state in free evolution. At last, the numerical simulations of the on-line state estimation of 2-qubit quantum systems are carried out in MATLAB environment, and the influences of the parameters on the estimation results are analyzed by the performance comparisons.

DOI
10.1109/med.2019.8798592

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A quantum state feedback control method is proposed in this paper. The state of a two-level open quantum system is estimated online based on the continuous weak measurement and the compressed sensing theory. Based on the state estimated online and the Lyapunov stability theorem, the state feedback control law used to transfer the quantum state is designed. Moreover, three numerical simulation experiments are implemented in the MATLAB environment: the state transfer from eigenstates to eigenstates, superposition states to superposition states, and superposition states to mixed states. The experimental results verify high performance of the proposed feedback control based on the state estimated online.
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Compressed sensing (CS) has been proved efficiently in reducing the required number of measurements in the quantum state estimation. In this paper, the relationship between the optimal number of measurement settings and the error of quantum state estimation via compressed sensing are studied by means of analyzing the lower bound of measurement settings and upper bound of error of quantum state estimation. Based on the results obtained by the CS theory, we analyze the above mentioned characteristics of three observation matrices and give the performance comparisons through the numerical simulations. The obtained optimal conditions and error bounds in the state estimation process can provide theoretical instructions for the selection of the minimum number of measurement settings in the quantum state estimation.
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