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.
In earlier work, we presented a formalism for reasoning about categorical models of quantum information REF .
Graphical reasoning in compact closed categories for quantum computation
Annals of Mathematics and Artificial Intelligence
Annals of Mathematics and Artificial Intelligence
Computer Science Mathematics