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Proceedings of the ... American Control Conference/Proceedings of the American Control Conference

Global stabilization at arbitrary eigenstates of N-dimensional quantum spin systems via continuous feedback

Koji Tsumura

Published Jun 1, 2008• 38 citations
Publisher

Abstract

In this paper, we deal with a stabilization problem on quantum spin systems in general dimensions. The spin systems are supposed under continuous measurement by mutual interference with laser beams and a magnetic field is applied for control. The quantum states of spin systems can be estimated by quantum filtering and the intension of the magnetic field is controlled according to the estimation. We show that the global stabilization at arbitrary eigenstates of the spin systems is possible by continuous control inputs. Our proposing control input is the sum of two terms: a term which attracts the quantum states to an objective eigenstate and the other term which draws apart from the other equilibrium points. We also demonstrate the results by a numerical simulation.

DOI
10.1109/acc.2008.4587144

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In this paper, we deal with a stabilization problem on quantum spin systems in general dimensions. The spin systems are supposed under continuous measurement by mutual interference with laser beams and a magnetic field is applied for control. The quantum states of spin systems can be estimated by quantum filtering and the intension of the magnetic field is controlled according to the estimation. We show that the global stabilization at arbitrary eigenstates of the spin systems is possible by continuous control inputs. Our proposing control input is the sum of two terms: a term which attracts the quantum states to an objective eigenstate and the other term which draws apart from the other equilibrium points. We also demonstrate the results by a numerical simulation.
In this paper, a stabilization problem of quantum spin systems in general dimension under continuous measurement is considered and it is shown that the global stabilization at an eigenstate by continuous inputs is possible. Quantum states of spin systems under continuous measurement by mutual interference with laser beams can be continuously estimated by quantum filtering and with its information, the intension of magnetic field, which is applied to atoms, can be controlled. Because of the structural symmetry of the nonlinear dynamics, this stabilization problem by continuous feedback has been considered to be hard and recently a switching rule was introduced which attains the global stability. Our proposing control rule is the sum of two terms: a term which attracts the quantum states to a target and the other term which draw apart from the other equilibrium points. The proof is done by the strict analysis on the sample paths of solutions of a stochastic differential equation. We also show numerical examples to demonstrate the efficiency of the proposing control rule.
In this paper, a stabilization problem of quantum spin systems in general dimension under continuous measurement is considered and it is shown that the global stabilization at an eigenstate by continuous inputs is possible. Quantum states of spin systems under continuous measurement by mutual interference with laser beams can be continuously estimated by quantum filtering and with its information, the intension of magnetic field, which is applied to atoms, can be controlled. Because of the structural symmetry of the nonlinear dynamics, this stabilization problem by continuous feedback has been considered to be hard and recently a switching rule was introduced which attains the global stability. Our proposing control rule is the sum of two terms: a term which attracts the quantum states to targets and the other term which draw apart from the other equilibrium points. The proof is done by the strict analysis on the sample paths of solutions of a stochastic differential equation. We also show numerical examples to demonstrate the efficiency of the proposing control rule.
In this chapter, we introduce our recent results on feedback control of quantum spin systems. The quantum systems are composed of atoms held in a cavity under continuous measurement by photons and a magnetic field that is applied to atoms for controlling the quantum states. The quantum states can be estimated by quan- tum filtering through the continuous measurement, and the intension of magnetic field is controlled depending on the estimations. We show that our proposing control input attains the global stability on the assigned eigenstates.
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.
In this paper, we consider stochastic master equations describing the evolutions of quantum systems interacting with electromagnetic fields undergoing continuous-time measurements. In particular, we study feedback control of quantum spin1/2 systems in the case of unawareness of initial states and in presence of measurement imperfections. We prove that the fidelity between the true quantum filter and its estimation (with arbitrary initial state) converges to one under appropriate assumption on the feedback controller. This shows the asymptotic convergence of such filters. In the more general case of spin-J systems, we discuss heuristically the asymptotic behavior of the true quantum filter and the associated estimation, and the possibility of exponentially stabilizing such systems towards an eigenvector of the measurement operator by an appropriate feedback.