Graphical reasoning in compact closed categories for quantum computation

  • Lucas DixonEmail author
  • Ross Duncan


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.


Graph rewriting Quantum computing Categorical logic Interactive theorem proving Graphical calculi Ellipses notation 

Mathematics Subject Classifications (2000)

03G30 18C10 03G12 05C20 81P68 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.University of EdinburghEdinburghUK
  2. 2.University of OxfordOxfordUK

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