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Transactions of the Institute of Systems Control and Information Engineers

Semi-Algebraic Problem Approach for Design of Quantum Spin Control Systems in the Face of Feedback Delay

Kenji Kashima

Published Jan 1, 2008• 0 citations
Publisher

Abstract

Accurate control of quantum spin is necessary in order to utilize quantum spin as the physical realization of the quantum bit. Feedback control (based on continuous quantum measurement) of quantum spin systems inevitably suffers from estimation delays. In this paper, we state that a control system which takes into account these delays can be described by using stochastic delay differential systems. Moreover, we can restrict our analysis to the class of systems which have polynomial coefficients and evolve in a bounded semi-algebraic set. Then, the problem of stabilizing such systems is shown to be solvable effectively via reduction to a semi-algebraic problem.

DOI
10.5687/iscie.21.111

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Accurate control of quantum spin is necessary in order to utilize quantum spin as the physical realization of the quantum bit. Feedback control (based on continuous quantum measurement) of quantum spin systems inevitably suffers from estimation delays. In this paper, we state that a control system which takes into account these delays can be described by using stochastic delay differential systems. Moreover, we can restrict our analysis to the class of systems which have polynomial coefficients and evolve in a bounded semi-algebraic set. Then, the problem of stabilizing such systems is shown to be solvable effectively via reduction to a semi-algebraic problem.
Feedback control (based on the quantum continuous measurement) of quantum systems inevitably suffers from estimation delays. In this technical note we give a delay-dependent stability criterion for a wide class of nonlinear stochastic systems including quantum spin systems. We utilize a semi-algebraic problem approach to incorporate the structure ofdensitymatrices. To show the effectiveness of the result, we derive a globally stabilizing control law for a quantum spin-1/2 systems in the face of feedback delays.
In this paper, feedback control of quantum spin systems is investigated. The quantum control scenario follows the formalism of continuous quantum measurement and quantum state estimation using the so-called stochastic master equation. In quantum feedback control implementations the state estimation is delayed, which is known to degrade the resulting control performance. As yet there are no theoretical means to take such estimation delays into consideration. In this paper we derive a stabilizing control law for two-dimensional quantum spin systems taking estimation delays into explicit account. From a control theoretic viewpoint, the obtained result is a delay-dependent stability criterion for a nonlinear stochastic switching system.
In this paper, feedback control of quantum spin systems is investigated. The quantum control scenario follows the formalism of continuous quantum measurement and quantum state estimation using the so-called stochastic master equation. In quantum feedback control implementations the state estimation is delayed, which is known to degrade the resulting control performance. As yet there are no theoretical means to take such estimation delays into consideration. In this paper we derive a globally stabilizing control law for two-dimensional quantum spin systems taking estimation delays into explicit account. From a control theoretic viewpoint, the obtained result is a delay-dependent stability criterion for a nonlinear stochastic switching system.
Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability.
This paper addresses the problem of measurement-based feedback control for quantum systems, in which the time to compute the filter-based control input is taken into account by considering the input delay. It starts with a new Lyapunov–LaSalle-like theorem for delay-dependent stochastic stability of a class of time delay stochastic nonlinear systems. Nonsmooth time delay control is then constructed to compensate for the control-computation time, which is known but arbitrarily long, while globally stabilizing the quantum filters almost surely. The nonsmooth property enables the control to deal with the symmetric topology of filter state space. The effectiveness of the proposed control is illustrated through the global stabilization of the spin-1/21/21/2 systems. Simulation results are presented and discussed to show the effectiveness of the proposed control.
Time delay is frequently encountered in practical quantum feedback control systems with long transmission lines and measurement process. This paper is concerned with measurement-based feedback H∞ control for quantum systems with time delays appearing in the feedback loops. A physical model is presented for the quantum time-delay system described by complex quantum stochastic differential equations. Quantum versions of some fundamental properties, such as dissipativity and stability, are discussed for this model. A numerical procedure is proposed for H∞ controller synthesis, which can deal with a non-convex optimization problem arising in the design processes. Copyright © 2016 John Wiley & Sons, Ltd.