Graphical reasoning in compact closed categories for quantum computation

• DOI: 10.1007/s10472-009-9141-x
• Publication Date: 2009-07-01T06:33:00Z
• Authors: Lucas Dixon; Ross Duncan
• Keywords: Formalism (music)

21 pages, 9 figures. This is the journal version of the paper published at AISC<br/>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 equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. 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.<br/>