Graphical Reasoning in Compact Closed Categories for Quantum Computation

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dc.creatorDixon, Lucas
dc.creatorDuncan, Ross
dc.date2009-02-03
dc.date.accessioned2026-07-07T12:37:18Z
dc.date.available2026-07-07T12:37:18Z
dc.descriptionCompact 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.
dc.description21 pages, 9 figures. This is the journal version of the paper published at AISC
dc.identifierhttps://arxiv.org/abs/0902.0514
dc.identifierhttp://arxiv.org/abs/0902.0514
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218396
dc.subjectSymbolic Computation
dc.subjectArtificial Intelligence
dc.titleGraphical Reasoning in Compact Closed Categories for Quantum Computation
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