Graphical Reasoning in Compact Closed Categories for Quantum Computation
Lucas Dixon and Ross Duncan 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 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.
infojournal | Annals of Mathematics and Artificial Intelligence |
keywords | categorical quantum mechanics; compact closed categories; rewriting; graphical calculi |
note | preprint available at http://arxiv.org/abs/0902.0514 |
year | 2009 |
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DOI (10.1007/s10472-009-9141-x)
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