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Entropy

State Transfer via On-Line State Estimation and Lyapunov-Based Feedback Control for a N-Qubit System

Sajede Harraz, Shuang Cong

Published Jul 31, 2019• 6 citations
Publisher

Abstract

In this paper, we propose a Lyapunov-based state feedback control for state transfer based on the on-line quantum state estimation (OQSE). The OQSE is designed based on continuous weak measurements and compressed sensing. The controlled system is described by quantum master equation for open quantum systems, and the continuous measurement operators are derived according to the dynamic equation of system. The feedback control law is designed based on the Lyapunov stability theorem, and a strict proof of proposed control laws are given. At each sampling time, the state is estimated on-line, which is used to design the control law. The simulation experimental results show the effectiveness of the proposed feedback control strategy.

DOI
10.3390/e21080751

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In this paper, we propose a Lyapunov-based state feedback control for state transfer based on the on-line quantum state estimation (OQSE). The OQSE is designed based on continuous weak measurements and compressed sensing. The controlled system is described by quantum master equation for open quantum systems, and the continuous measurement operators are derived according to the dynamic equation of system. The feedback control law is designed based on the Lyapunov stability theorem, and a strict proof of proposed control laws are given. At each sampling time, the state is estimated on-line, which is used to design the control law. The simulation experimental results show the effectiveness of the proposed feedback control strategy.
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
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.
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.
The weak-coupled two-level open quantum system described by non-Markovian time-convolution-less master equation is investigated in this paper. Based on the Lyapunov stability theorem, the system control laws used to transfer state are designed. The characteristics of the purity changes in the non-Markovian open quantum systems are studied. The effectiveness of the control system is ensured by adjusting the parameters of control laws. Three simulation experiments are implemented under the Matlab environment, they are the states transfer from the eigenstate to the superposition state, from the superposition state to the superposition state, and from the mixed state to the superposition state, respectively. Numerical experimental results show that the target state can be reached from different initial states under the action of the control laws designed, and demonstrate the effectiveness of quantum Lyapunov control method proposed.
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.