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Graphical reasoning in compact closed categories for quantum computation

Graphical reasoning in compact closed categories for quantum computation Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for reasoning about compact closed categories. A salient feature of our system is that it provides a formal and declarative account of derived results that can include ‘ellipses’-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Graphical reasoning in compact closed categories for quantum computation

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References (40)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer Science+Business Media B.V.
Subject
Computer Science; Statistical Physics, Dynamical Systems and Complexity; Mathematics, general; Computer Science, general; Artificial Intelligence (incl. Robotics)
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-009-9141-x
Publisher site
See Article on Publisher Site

Abstract

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for reasoning about compact closed categories. A salient feature of our system is that it provides a formal and declarative account of derived results that can include ‘ellipses’-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Jul 2, 2009

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