A geometrical approach to quantum holonomic computing algorithms

Document Type

Article

Publication Date

6-4-2004

Abstract

The article continues a presentation of modern quantum mathematics backgrounds started in [Quantum Mathematics and its Applications. Part 1. Automatyka, vol. 6, AGH Publisher, Krakow, 2002, No. 1, pp. 234-2412; Quantum Mathematics: Holonomic Computing Algorithms and Their Applications. Part 2. Automatyka, vol. 7, No. 1, 2004]. A general approach to quantum holonomic computing based on geometric Lie-algebraic structures on Grassmann manifolds and related with them Lax type flows is proposed. Making use of the differential geometric techniques like momentum mapping reduction, central extension and connection theory on Stiefel bundles it is shown that the associated holonomy groups properly realizing quantum computations can be effectively found concerning diverse practical problems. Two examples demonstrating two-form curvature calculations important for describing the corresponding holonomy Lie algebra are presented in detail. © 2004 IMACS. Published by Elsevier B.V. All rights reserved.

Identifier

2542497040 (Scopus)

Publication Title

Mathematics and Computers in Simulation

External Full Text Location

https://doi.org/10.1016/j.matcom.2004.01.017

ISSN

03784754

First Page

1

Last Page

20

Issue

1

Volume

66

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