The basic rewrite theory behind Quantomatic
- Aleks Kissinger. Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing, DPhil thesis, [arXiv:1203.0202]
- Lucas Dixon, Aleks Kissinger. Open Graphs and Monoidal Theories, [arXiv:1011.4114]
- Lucas Dixon, Ross Duncan, A. Kissinger. Open Graphs and Computational Reasoning, DCM 2010 [12 pages, pdf]
- Lucas Dixon and Aleks Kissinger. Monoidal Categories, Graphical Reasoning, and Quantum Computation, Extended Abstract [14 pages, 2009, pdf].
- Lucas Dixon and Ross Duncan. Graphical Reasoning in Compact Closed Categories for Quantum Computation, AMAI, special issue on AISC 2008 [20 pages, 2008, pdf, Springer].
- Lucas Dixon and Ross Duncan. Extending Graphical Representations for Compact Closed Categories with Applications to Symbolic Quantum Computation, AISC 2008 [16 pages, 2008 pdf]. (Note the journal article in AMAI, above, makes significant improvements on this paper - read that instead)
!-graphs and !-graph rewriting
- Alexander Merry. Reasoning with !-Graphs, DPhil thesis, [arXiv:1403.7828]
- Aleks Kissinger, Alex Merry, Matvey Soloviev. Pattern Graph Rewrite Systems, DCM 2012, [arXiv:1204.6695]
Applications of graphical theories
- Bob Coecke and Ross Duncan. Interacting Quantum Observables: Categorical Algebra and Diagrammatics, New J. Physics 13 (2011) 043016, [arXiv:0906.4725]
- Ross Duncan, Simon Perdrix. Rewriting Measurement-Based Quantum Computations with Generalised Flow., ICALP 2010 [12 pages, springer]
- Bob Coecke and Aleks Kissinger. The compositional structure of multipartite quantum entanglement, ICALP 2010. [arXiv:1002.2540]
- Ross Duncan and Simon Perdrix. Graph States and the necessity of Euler Decomposition, Computability in Europe: Mathematical Theory and Computational Practice (CiE'09). [arXiv:0902.0500]
- Bob Coecke and Ross Duncan. Interacting Quantum Observables, ICALP 2008, [arXiv:0906.4725] (Note: the journal article above supersedes this paper. Read that instead.)
- Aleks Kissinger. Exploring a Quantum Theory with Graph Rewriting and Computer Algebra, LNCS proceedings of Calculemus 2009 [15 pages, 2009, pdf].
- Lucas Dixon, Ross Duncan and Aleks Kissinger, Graph Rewriting for Classical Structures, Poster Presented at QICS 2008 [A0 poster, 2008, pdf].
- Introduction and demo of Quantomatic (20 minute Oxford computing lab video), presented by Lucas Dixon at the QICS Summer School (see also the other videos from QICS) held at the University of Oxford, May 2010.
- Graphical Reasoning in Symmetric Monoidal Categories for Quantum Information. Lucas Dixon. [slides as pdf, 1hr with demo] Invited talk for The Wednesday Seminar, University of Cambridge, 27 Jan 2010.
- Graphical reasoning in symmetric monoidal categories. Lucas Dixon. Invited talk at University of Leicester, 5 Nov 2009 [pdf]
- Monoidal Theories and Graph Rewriting in Quantum Computing. Aleks Kissenger and Lucas Dixon. At CAM-CAD, 17 Oct 2009 [pdf]
- Quantum CS with Graph Rewriting and CAS. Aleks Kissenger. Calculemus, 6 Jul 2009 [pdf]
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