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Extending Graphical Representations for Compact Closed Categories with Applications to Symbolic Quantum Computation

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Intelligent Computer Mathematics (CICM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5144))

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Abstract

Graph-based formalisms of quantum computation provide an abstract and symbolic way to represent and simulate computations. However, manual manipulation of such graphs is slow and error prone. We present a formalism, based on compact closed categories, that supports mechanised reasoning about such graphs. This gives a compositional account of graph rewriting that preserves the underlying categorical semantics. Using this representation, we describe a generic system with a fixed logical kernel that supports reasoning about models of compact closed category. A salient feature of the 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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Serge Autexier John Campbell Julio Rubio Volker Sorge Masakazu Suzuki Freek Wiedijk

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Dixon, L., Duncan, R. (2008). Extending Graphical Representations for Compact Closed Categories with Applications to Symbolic Quantum Computation. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85110-3_8

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  • DOI: https://doi.org/10.1007/978-3-540-85110-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85109-7

  • Online ISBN: 978-3-540-85110-3

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