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Lecture notes in physics

Controlled Systems

Gernot Schaller

Published Jan 1, 2014• 0 citations
Publisher
DOI
10.1007/978-3-319-03877-3_7

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This paper discusses fully coherent quantum feedback control, in which the sensors, controller, and actuators are quantum systems and interact coherently with the system to be controlled: as a result, the entire feedback loop is coherent. Unlike conventional semiclassical feedback control of quantum systems, feedback control by quantum controllers is not stochastic, preserves the initial state of the controlled system, and can control quantum systems in ways that are not possible using conventional, incoherent feedback control. In particular, the target state to which the quantum controller drives the system can be entangled with another quantum system. This paper investigates quantum controllers and states necessary and sufficient conditions for a Hamiltonian quantum system to be observable and controllable by a quantum controller.
This article focuses on wavefunction controllability of a class of quantum systems with switching control. First, we present a specific quantum system which is not wavefunction controllable under the action of any one of two controllers with different fixed structures. However, we prove that the system is wavefunction controllable if the control input is allowed to switch between the two controllers. Then we present a sufficient condition for wavefunction controllability of a class of quantum systems with switching control and briefly discuss the problem of control design for such quantum control systems. Finally, two illustrative examples are presented to demonstrate a possible control design process for the proposed method.
A pure indirect control of quantum systems via quantum accessor is investigated. In this control scheme, we do not apply any external classical excitation fields on the controlled system and we control a quantum system via a quantum accessor and classical control fields control the accessor only. Complete controllability is investigated for arbitrary finite dimensional quantum systems and exemplified by 2 and 3 dimensional systems. The scheme exhibits some advantages; it uses less qubits in accessor and does not depend on the energy-level structure of the controlled system.