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