Exploring a Quantum Theory with Graph Rewriting and Computer Algebra

Graphical languages provide a powerful tool for describing the behaviour of quantum systems. While the use of graphs vastly reduces the complexity of many calculations [4,10], manual graphical manipulation quickly becomes untenable for large graphs or large numbers of graphs. To combat this issue, we are developing a tool called Quantomatic, which allows automated and semi-automated explorations of graph rewrite systems and their underlying semantics. We emphasise in this paper the features of Quantomatic that interact with a computer algebra system to discover graphical relationships via the unification of matrix equations. Since these equations can grow exponentially with the size of the graph, we use this method to discover small identities and use those identities as graph rewrites to expand the theory.

• Type: Conference
• Year: 2009
• Where: MKM
• Authors: Aleks Kissinger
• Keywords: Graph Rewrites, Graphical, Information Management, Manual Graphical Manipulation, MKM 2009