Back and forth nudging for quantum state estimation by continuous weak measurement

Zaki Leghtas; Mazyar Mirrahimi; Pierre Rouchon

doi:10.1109/acc.2011.5991108

Back and forth nudging for quantum state estimation by continuous weak measurement

Zaki Leghtas
, Mazyar Mirrahimi
, Pierre Rouchon

École Polytechnique

INRIA Institut National de Recherche en Informatique et en Automatique
Mines ParisTech

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

Abstract

We propose to apply the Back and Forth Nudging (BFN) method used for geophysical data assimilations [1] to estimate the initial state of a quantum system. We consider a cloud of atoms interacting with a magnetic field while a single observable is being continuously measured over time using homodyne detection. The BFN method relies on designing an observer forward and backwards in time. The state of the BFN observer is continuously updated by the measured data and tends to converge to the system's state. The proposed estimator seems to be globally asymptotically convergent when the system is observable. A detailed convergence proof and simulations are given in the 2-level case. An extension of the algorithm to the multilevel case is also presented.

Original language	English
Title of host publication	Proceedings of the 2011 American Control Conference, ACC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4334-4339
Number of pages	6
ISBN (Print)	9781457700804
DOIs	https://doi.org/10.1109/acc.2011.5991108
Publication status	Published - 1 Jan 2011

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

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10.1109/acc.2011.5991108

Cite this

Leghtas, Z., Mirrahimi, M., & Rouchon, P. (2011). Back and forth nudging for quantum state estimation by continuous weak measurement. In Proceedings of the 2011 American Control Conference, ACC 2011 (pp. 4334-4339). Article 5991108 (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2011.5991108

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abstract = "We propose to apply the Back and Forth Nudging (BFN) method used for geophysical data assimilations [1] to estimate the initial state of a quantum system. We consider a cloud of atoms interacting with a magnetic field while a single observable is being continuously measured over time using homodyne detection. The BFN method relies on designing an observer forward and backwards in time. The state of the BFN observer is continuously updated by the measured data and tends to converge to the system's state. The proposed estimator seems to be globally asymptotically convergent when the system is observable. A detailed convergence proof and simulations are given in the 2-level case. An extension of the algorithm to the multilevel case is also presented.",

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Back and forth nudging for quantum state estimation by continuous weak measurement. / Leghtas, Zaki; Mirrahimi, Mazyar; Rouchon, Pierre.
Proceedings of the 2011 American Control Conference, ACC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 4334-4339 5991108 (Proceedings of the American Control Conference).

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

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AU - Mirrahimi, Mazyar

AU - Rouchon, Pierre

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Y1 - 2011/1/1

N2 - We propose to apply the Back and Forth Nudging (BFN) method used for geophysical data assimilations [1] to estimate the initial state of a quantum system. We consider a cloud of atoms interacting with a magnetic field while a single observable is being continuously measured over time using homodyne detection. The BFN method relies on designing an observer forward and backwards in time. The state of the BFN observer is continuously updated by the measured data and tends to converge to the system's state. The proposed estimator seems to be globally asymptotically convergent when the system is observable. A detailed convergence proof and simulations are given in the 2-level case. An extension of the algorithm to the multilevel case is also presented.

AB - We propose to apply the Back and Forth Nudging (BFN) method used for geophysical data assimilations [1] to estimate the initial state of a quantum system. We consider a cloud of atoms interacting with a magnetic field while a single observable is being continuously measured over time using homodyne detection. The BFN method relies on designing an observer forward and backwards in time. The state of the BFN observer is continuously updated by the measured data and tends to converge to the system's state. The proposed estimator seems to be globally asymptotically convergent when the system is observable. A detailed convergence proof and simulations are given in the 2-level case. An extension of the algorithm to the multilevel case is also presented.

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M3 - Conference contribution

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BT - Proceedings of the 2011 American Control Conference, ACC 2011

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ER -

Back and forth nudging for quantum state estimation by continuous weak measurement

Abstract

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