Global stabilization of two-dimensional quantum spin systems despite estimation delay

Kenji Kashima; Kazunori Nishio

doi:10.1109/CDC.2007.4434611

Global stabilization of two-dimensional quantum spin systems despite estimation delay

Kenji Kashima, Kazunori Nishio

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 Citations (Scopus)

Abstract

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.

Original language	English
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6352-6357
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434611
Publication status	Published - 2007
Externally published	Yes
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: 2007 Dec 12 → 2007 Dec 14

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	07/12/12 → 07/12/14

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2007.4434611

Cite this

Kashima, K., & Nishio, K. (2007). Global stabilization of two-dimensional quantum spin systems despite estimation delay. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 6352-6357). [4434611] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2007.4434611

Global stabilization of two-dimensional quantum spin systems despite estimation delay. / Kashima, Kenji; Nishio, Kazunori.

Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 6352-6357 4434611 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kashima, K & Nishio, K 2007, Global stabilization of two-dimensional quantum spin systems despite estimation delay. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434611, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 6352-6357, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 07/12/12. https://doi.org/10.1109/CDC.2007.4434611

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AB - 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.

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Global stabilization of two-dimensional quantum spin systems despite estimation delay

Abstract

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ASJC Scopus subject areas

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