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International Conference on Software and Information Engineering (ICSIE)

Quantum State Feedback Control Based on the on-line State Estimation

Yaru Tang, Shuang Cong

Published Apr 9, 2019• 0 citations
Publisher

Abstract

In this paper the state of Markovian open quantum system is estimated on-line based on the continuous weak measurement and compression sensing theory, and a quantum Lyapunov feedback control law is designed to transfer the state from the initial state to the desired target state based on the state estimated on-line. Numerical simulation experiments are implemented under MATLAB environment. The experimental results show the effectiveness of the on-line estimated state-based feedback control method proposed

DOI
10.1145/3328833.3328839

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In this paper the state of Markovian open quantum system is estimated on-line based on the continuous weak measurement and compression sensing theory, and a quantum Lyapunov feedback control law is designed to transfer the state from the initial state to the desired target state based on the state estimated on-line. Numerical simulation experiments are implemented under MATLAB environment. The experimental results show the effectiveness of the on-line estimated state-based feedback control method proposed
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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.
For thennn-qubit stochastic open quantum systems, based on the Lyapunov stability theorem and LaSalle's invariant set principle, a pure state switching control based on on-line estimated state feedback (short for OQST-SFC) is proposed to realize the state transition the pure state of the target state including eigenstate and superposition state. The proposed switching control consists of a constant control and a control law designed based on the Lyapunov method, in which the Lyapunov function is the state distance of the system. The constant control is used to drive the system state from an initial state to the convergence domain only containing the target state, and a Lyapunov-based control is used to make the state enter the convergence domain and then continue to converge to the target state. At the same time, the continuous weak measurement of quantum system and the quantum state tomography method based on the on-line alternating direction multiplier (QST-OADM) are used to obtain the system information and estimate the quantum state which is used as the input of the quantum system controller. Then, the pure state feedback switching control method based on the on-line estimated state feedback is realized in annnn-qubit stochastic open quantum system. The complete derivation process ofnnn-qubit QST-OADM algorithm is given; Through strict theoretical proof and analysis, the convergence conditions to ensure any initial state of the quantum system to converge the target pure state are given. The proposed control method is applied to a 2-qubit stochastic open quantum system for numerical simulation experiments. Four possible different position cases between the initial estimated state and that of the controlled system are studied and discussed, and the performances of the state transition under the corresponding cases are analyzed.
Abstract An online estimated state feedback control for trajectory tracking in stochastic open quantum systems is proposed in this paper, which is based on the Lyapunov‐based control method. By inducing the error between the controlled state, and the target state as the error state, the trajectory tracking problem of the quantum system is transformed into the error state transition control problem. The quantum state online estimation method QST‐OADM is applied to estimate the state of the error state system online, and the tracking control laws are designed by using the quantum Lyapunov stability theorem for driving the stochastic open quantum system from an arbitrary initial state to an arbitrary trajectory. The numerical simulation experiments and results analyses are given.
In this paper, a nonlinear optimal feedback control based on the nonlinear state estimator for a two-level open non-Markovian stochastic quantum system is proposed. The proposed nonlinear state estimator is designed by using the state-dependent differential Riccati equation and constructed to optimally estimate the state. The estimated state is updated by the output data of continuous weak measurement of the controlled quantum system and used to design the nonlinear state feedback controller to track the output of the reference model. The output state of reference model is chosen as the desired performance. The numerical simulation results verify the achievability of the proposed state feedback control strategy, and the capability to steer the state of system from any arbitrary initial state to the final reference target state with high state transfer success rate.
This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems, with the main analysis focused on finite-dimensional systems governed by diffusive stochastic master equations. We introduce the relevant state-space, invariant-subspace, and quantum non-demolition structures, interpret quantum filtering as nonlinear observer dynamics, and review open-loop asymptotics, filter stability, state-feedback stabilization, robustness, and reduced-order observer-based control. Particular emphasis is placed on a recurrence--contraction framework, in which Hamiltonian feedback removes non-target invariant obstructions while measurement-induced dynamics provide local exponential contraction. Although the detailed analysis is developed for finite-dimensional diffusive models, the underlying measurement--estimation--feedback architecture is relevant across a broad range of quantum platforms. We further discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics, practical stability, optimal control, and learning-based design. By organizing these developments around invariance, estimation, recurrence, and contraction, the review provides a tutorial bridge between measurement-based quantum feedback and nonlinear stochastic control.