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Abstract
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.
Original language | English |
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Pages (from-to) | 23-42 |
Number of pages | 20 |
Journal | Annals of Mathematics and Artificial Intelligence |
Volume | 56 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2009 |
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Dive into the research topics of 'Graphical reasoning in compact closed categories for quantum computation'. Together they form a unique fingerprint.Projects
- 1 Finished
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Integration and Interaction of multiple mathematical reasoning processes
Bundy, A., Colton, S., Aspinall, D., Dennis, L., Fleuriot, J., Georgieva, L., Ireland, A., Jackson, P. & Smaill, A.
1/04/07 → 31/03/11
Project: Research