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Computational and control aspects of...
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Lucarelli, Dennis Gary.
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Computational and control aspects of quantum holonomy.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Computational and control aspects of quantum holonomy./
作者:
Lucarelli, Dennis Gary.
面頁冊數:
104 p.
附註:
Source: Dissertation Abstracts International, Volume: 64-03, Section: B, page: 1469.
Contained By:
Dissertation Abstracts International64-03B.
標題:
Engineering, System Science. -
電子資源:
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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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.
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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.
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