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Title:Graphical Reasoning in Compact Closed Categories for Quantum Computation
Authors: Lucas Dixon ; Ross Duncan
Date: 2008
Publication Title:Annals of Mathematics and Artificial Intelligence
Publication Type:Journal Article Publication Status:Submitted
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 equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. 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.
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Bibtex format
author = { Lucas Dixon and Ross Duncan },
title = {Graphical Reasoning in Compact Closed Categories for Quantum Computation},
journal = {Annals of Mathematics and Artificial Intelligence},
publisher = {Springer},
year = 2008,
url = {},

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