Ensemble controllability of the bloch equations

Jr Shin Li; Navin Khaneja

doi:10.1109/cdc.2006.377454

Ensemble controllability of the bloch equations

Jr Shin Li, Navin Khaneja

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

13 Scopus citations

Abstract

Finding control fields (pulse sequences) that can compensate for the dispersion in the parameters governing the evolution of a quantum system is an important problem in coherent spectroscopy and quantum information processing. The use of composite pulses for compensating dispersions in system dynamics is widely known and applied. In this paper, we make explicit the key aspects of the dynamics that make such a compensation possible. We highlight the role of Lie algebras and non-commutativity in the design of a compensating pulse sequence. Finally, we investigate three common dispersions in NMR spectroscopy, the Larmor dispersion, rf inhomogeneity and the strength of couplings between the spins.

Original language	English
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2483-2487
Number of pages	5
ISBN (Print)	1424401712, 9781424401710
DOIs	https://doi.org/10.1109/cdc.2006.377454
State	Published - 2006
Event	45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: Dec 13 2006 → Dec 15 2006

Publication series

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

Conference

Conference	45th IEEE Conference on Decision and Control 2006, CDC
Country/Territory	United States
City	San Diego, CA
Period	12/13/06 → 12/15/06

Access to Document

10.1109/cdc.2006.377454

Cite this

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title = "Ensemble controllability of the bloch equations",

abstract = "Finding control fields (pulse sequences) that can compensate for the dispersion in the parameters governing the evolution of a quantum system is an important problem in coherent spectroscopy and quantum information processing. The use of composite pulses for compensating dispersions in system dynamics is widely known and applied. In this paper, we make explicit the key aspects of the dynamics that make such a compensation possible. We highlight the role of Lie algebras and non-commutativity in the design of a compensating pulse sequence. Finally, we investigate three common dispersions in NMR spectroscopy, the Larmor dispersion, rf inhomogeneity and the strength of couplings between the spins.",

author = "Li, {Jr Shin} and Navin Khaneja",

year = "2006",

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language = "English",

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series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "2483--2487",

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note = "45th IEEE Conference on Decision and Control 2006, CDC ; Conference date: 13-12-2006 Through 15-12-2006",

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Li, JS & Khaneja, N 2006, Ensemble controllability of the bloch equations. in Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC., 4177466, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2483-2487, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 12/13/06. https://doi.org/10.1109/cdc.2006.377454

Ensemble controllability of the bloch equations. / Li, Jr Shin; Khaneja, Navin.
Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc., 2006. p. 2483-2487 4177466 (Proceedings of the IEEE Conference on Decision and Control).

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

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N2 - Finding control fields (pulse sequences) that can compensate for the dispersion in the parameters governing the evolution of a quantum system is an important problem in coherent spectroscopy and quantum information processing. The use of composite pulses for compensating dispersions in system dynamics is widely known and applied. In this paper, we make explicit the key aspects of the dynamics that make such a compensation possible. We highlight the role of Lie algebras and non-commutativity in the design of a compensating pulse sequence. Finally, we investigate three common dispersions in NMR spectroscopy, the Larmor dispersion, rf inhomogeneity and the strength of couplings between the spins.

AB - Finding control fields (pulse sequences) that can compensate for the dispersion in the parameters governing the evolution of a quantum system is an important problem in coherent spectroscopy and quantum information processing. The use of composite pulses for compensating dispersions in system dynamics is widely known and applied. In this paper, we make explicit the key aspects of the dynamics that make such a compensation possible. We highlight the role of Lie algebras and non-commutativity in the design of a compensating pulse sequence. Finally, we investigate three common dispersions in NMR spectroscopy, the Larmor dispersion, rf inhomogeneity and the strength of couplings between the spins.

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Ensemble controllability of the bloch equations

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