2002
DOI: 10.1155/s1110757x02110163
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Introduction to Grassmann manifolds and quantum computation

Abstract: Geometrical aspects of quantum computing are reviewed elementarily for nonexperts and/or graduate students who are interested in both geometry and quantum computation. We show how to treat Grassmann manifolds which are very important examples of manifolds in mathematics and physics. Some of their applications to quantum computation and its efficiency problems are shown. An interesting current topic of holonomic quantum computation is also covered. Also, some related advanced topics are discussed.

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Cited by 36 publications
(37 citation statements)
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“…In this letter we studied the B-C-H formula for the case of SO (4) Physics moreover, see for example [10], [11].…”
Section: Discussionmentioning
confidence: 99%
“…In this letter we studied the B-C-H formula for the case of SO (4) Physics moreover, see for example [10], [11].…”
Section: Discussionmentioning
confidence: 99%
“…Fujii [15], [16] in the context of Holonomic Quantum Computation. In a forthcoming paper we want to point out a deeper relation between the gauge theory and some quantum computation (Cavity QED quantum computation if possible).…”
Section: Discussionmentioning
confidence: 99%
“…As another definition of the Grassmann manifold the following one in terms of projections is also well-known. See [5] and [6] as an elementery introduction and [7] as an advanced one.…”
Section: Reduced Dynamics On Grassmann Manifolds : Reviewmentioning
confidence: 99%