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Computational and control aspects of...

Lucarelli, Dennis Gary.

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Computational and control aspects of quantum holonomy.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Computational and control aspects of quantum holonomy./
Author:	Lucarelli, Dennis Gary.
Description:	104 p.
Notes:	Source: Dissertation Abstracts International, Volume: 64-03, Section: B, page: 1469.
Contained By:	Dissertation Abstracts International64-03B.
Subject:	Engineering, System Science. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3083577
ISBN:	9780496313853

Computational and control aspects of quantum holonomy.
Lucarelli, Dennis Gary.

Computational and control aspects of quantum holonomy. - 104 p.

Source: Dissertation Abstracts International, Volume: 64-03, Section: B, page: 1469.

Thesis (D.Sc.)--Washington University, 2002.

Geometric phases have long been a source of fascination and insight into classical and quantum physical theories. Geometric methods have also made a profound impact in the field of engineering. Inspired by the appearance of geometric phases in biology, engineers have sought to create motion in machines via cyclic variations in shape space. Recently, geometric phases have been proposed as a way of constructing logic gates in a quantum computer. Geometric quantum computation employs non-Abelian holonomies to do quantum logic processing.

ISBN: 9780496313853Subjects--Topical Terms:

1018128
Engineering, System Science.

Computational and control aspects of quantum holonomy.
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020 $a 9780496313853
035 $a (UnM)AAI3083577
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040 $a UnM $c UnM
100 1 $a Lucarelli, Dennis Gary. $3 1912418
245 1 0 $a Computational and control aspects of quantum holonomy.
300 $a 104 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-03, Section: B, page: 1469.
500 $a Director: T. J. Tarn.
502 $a Thesis (D.Sc.)--Washington University, 2002.
520 $a Geometric phases have long been a source of fascination and insight into classical and quantum physical theories. Geometric methods have also made a profound impact in the field of engineering. Inspired by the appearance of geometric phases in biology, engineers have sought to create motion in machines via cyclic variations in shape space. Recently, geometric phases have been proposed as a way of constructing logic gates in a quantum computer. Geometric quantum computation employs non-Abelian holonomies to do quantum logic processing.
520 $a In this dissertation, a comprehensive theory for the control of quantum systems with non-Abelian holonomy is presented. By exploiting the rich geometry of principal bundles with connection, insight may be gained into the control theoretic properties of such systems. The well developed theory of control systems evolving on principal bundles is useful in treating the controllability as well as the constructive controllability problems for quantum holonomic systems. Problems arising in geometric quantum computation are cast within this framework to obtain new results for systems with the conditional Berry phase and systems based on squeezed coherent states. For these systems, we characterize the reachable set and then use the Cartan decomposition of compact Lie groups to completely solve the constructive controllability problem. Control laws, obtained in this way, can then be used to implement quantum algorithms. Robustness of the model and entanglement as a computational resource are touched upon.
590 $a School code: 0252.
650 4 $a Engineering, System Science. $3 1018128
650 4 $a Mathematics. $3 515831
690 $a 0790
690 $a 0405
710 2 0 $a Washington University. $3 1250147
773 0 $t Dissertation Abstracts International $g 64-03B.
790 1 0 $a Tarn, T. J., $e advisor
790 $a 0252
791 $a D.Sc.
792 $a 2002
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3083577