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Graphical reasoning in compact closed categories for quantum computation

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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.

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Authors and Affiliations

  1. University of Edinburgh, Edinburgh, UK

    Lucas Dixon

  2. University of Oxford, Oxford, UK

    Ross Duncan

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  1. Lucas Dixon
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  2. Ross Duncan
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Correspondence to Lucas Dixon.

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Dixon, L., Duncan, R. Graphical reasoning in compact closed categories for quantum computation. Ann Math Artif Intell 56, 23–42 (2009). https://doi.org/10.1007/s10472-009-9141-x

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  • DOI: https://doi.org/10.1007/s10472-009-9141-x

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