papers.html

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title: Papers
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<h1>Papers</h1>

<!-- <p>For a study of an example of the graphical languages Quantomatic is designed for working with, read <i>Interacting Quantum Observables: Categorical Algebra and Diagrammatics</i> [Coecke, Duncan 2011, <a href="http://arxiv.org/abs/0906.4725">arXiv:0906.4725</a>].  Another example is given in <i>The compositional structure of multipartite quantum entanglement</i>, [Coecke, Kissinger 2010, <a href="http://arxiv.org/abs/1002.2540">arXiv:1002.2540</a>]</p><p>Much of the theory underpinning Quantomatic can be either picked out of Aleks Kissinger's thesis [Kissinger 2011, <a href="http://arxiv.org/abs/1203.0202">arXiv:1203.0202</a>], or read in <i>Open Graphs and Monoidal Theories</i>, [Dixon, Kissinger 2010 <a href="http://arxiv.org/abs/1011.4114">arXiv:1011.4114</a>] (although note that some of the terminology has changed). !-boxes are formalised in <i>Pattern Graph Rewrite Systems</i>, [Kissinger, Merry, Soloviev 2012, <a href="http://arxiv.org/abs/1204.6695">arXiv:1204.6695</a>].</p> -->


<h2>The basic rewrite theory behind Quantomatic</h2>

<ul>

<li>Aleks Kissinger. <i>Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing</i>, DPhil thesis, [<a href="http://arxiv.org/abs/1203.0202">arXiv:1203.0202</a>]<br /></li>

<li>Lucas Dixon, Aleks Kissinger. <i>Open Graphs and Monoidal Theories</i>, [<a href="http://arxiv.org/abs/1011.4114">arXiv:1011.4114</a>]<br /></li>

<li>Lucas Dixon, Ross Duncan, A. Kissinger. <i>Open Graphs and Computational Reasoning</i>, <a href="http://www.amsta.leeds.ac.uk/%7Epmt6sbc/DCM10/">DCM
2010</a> [12 pages, <a href="http://homepages.inf.ed.ac.uk/ldixon/papers/open-graphs1.pdf">pdf</a>] </li>

<li>Lucas Dixon and Aleks Kissinger. <i>Monoidal Categories, Graphical
Reasoning, and Quantum Computation</i>, Extended Abstract
[14 pages,
2009, <a href="http://dream.inf.ed.ac.uk/projects/quantomatic/papers/dixon-kissinger-camcad-09.pdf">pdf</a>].</li>

<li>Lucas Dixon and Ross Duncan. <i>Graphical Reasoning in
Compact Closed Categories for Quantum Computation</i>, AMAI, special issue on AISC 2008 [20 pages, 2008, <a href="http://dream.inf.ed.ac.uk/projects/quantomatic/papers/reasoning-graphically-amai08.pdf">pdf</a>, <a href="http://www.springerlink.com/content/m324n52316r3t250/">Springer</a>].</li>

<li>Lucas Dixon and Ross Duncan. <i>Extending Graphical Representations
for Compact Closed Categories with Applications to Symbolic Quantum
Computation</i>, AISC 2008 [16 pages, 2008 <a href="http://dream.inf.ed.ac.uk/projects/quantomatic/papers/quantomatic-aisc08.pdf">pdf</a>]. (Note the
journal article in AMAI, above, makes significant improvements on this
paper - read that instead)</li>

</ul>


<h2>!-graphs and !-graph rewriting</h2>


<ul>

<li>Alexander Merry. <i>Reasoning with !-Graphs</i>, DPhil thesis, [<a href="http://arxiv.org/abs/1403.7828">arXiv:1403.7828</a>]<br /></li>

<li>Aleks Kissinger, Alex Merry, Matvey Soloviev. <i>Pattern Graph Rewrite Systems</i>, DCM 2012, [<a href="http://arxiv.org/abs/1204.6695">arXiv:1204.6695</a>]<br /></li>

</ul>


<h2>Applications of graphical theories</h2>


<ul>

<li>Bob Coecke and Ross Duncan. <i>Interacting Quantum Observables: Categorical Algebra and Diagrammatics</i>, <a href="http://iopscience.iop.org/1367-2630/13/4/043016/">New J. Physics 13 (2011) 043016</a>, [<a href="http://arxiv.org/abs/0906.4725">arXiv:0906.4725</a>]</li>


<li>Ross Duncan, Simon Perdrix. <i>Rewriting Measurement-Based Quantum Computations with Generalised Flow.</i>, <a href="http://icalp10.inria.fr/">ICALP
2010</a> [12 pages, <a href="http://www.springerlink.com/content/06g573327343gq75/">springer</a>] </li>


<li>Bob Coecke and Aleks Kissinger. <i>The compositional structure of multipartite quantum entanglement</i>, <a href="http://icalp10.inria.fr/">ICALP 2010</a>. [<a href="http://arxiv.org/abs/1002.2540">arXiv:1002.2540</a>]</li>

<li>Ross Duncan and Simon Perdrix. <i>Graph States and the necessity of Euler Decomposition</i>, <a href="http://www.illc.uva.nl/CiE/index.php?page=_5">Computability in Europe: Mathematical Theory and Computational Practice (CiE'09)</a>. [<a href="http://arxiv.org/abs/0902.0500">arXiv:0902.0500</a>]</li>

<li>Bob Coecke and Ross Duncan. <i>Interacting Quantum Observables</i>, <a href="http://www2.ru.is/icalp08/">ICALP 2008</a>, [<a href="http://arxiv.org/abs/0906.4725">arXiv:0906.4725</a>]  (Note: the journal article above supersedes this paper.  Read that instead.)</li>

<li>Aleks Kissinger. <i>Exploring a Quantum Theory with Graph Rewriting and Computer Algebra</i>, LNCS proceedings of Calculemus 2009 [15 pages, 2009, <a href="http://www.comlab.ox.ac.uk/people/Aleks.Kissinger/download/kissinger09_cmus.pdf">pdf</a>].</li>

</ul>


<h1>Posters</h1>

<ul>

<li>Lucas Dixon, Ross Duncan and Aleks Kissinger, <i>Graph Rewriting for Classical Structures</i>, Poster Presented at
QICS 2008 [A0 poster, 2008, <a href="http://dream.inf.ed.ac.uk/projects/quantomatic/posters/poster-QICS-08.pdf">pdf</a>].</li>

</ul>


<h1>Talks</h1>


<ul>

<li>Introduction and demo of Quantomatic (20 minute <a href="http://www.comlab.ox.ac.uk/quantum/content/1005019/">Oxford computing
lab video</a>), presented by Lucas Dixon at the <a href="http://www.comlab.ox.ac.uk/people/Bob.Coecke/QICS_School.html">QICS
Summer School</a> (see also the <a href="http://www.comlab.ox.ac.uk/quantum/content/events.html#QICS%20spring%20school%202010">other
videos from QICS</a>) held at the University of Oxford, May 2010. </li>

<li><i>Graphical Reasoning in Symmetric Monoidal Categories for Quantum Information</i>. Lucas Dixon.  [<a href="http://dream.inf.ed.ac.uk/projects/quantomatic/talks/cambridge-2010-2x2.pdf">slides
as pdf</a>, 1hr with demo] Invited talk for <a href="http://www.cl.cam.ac.uk/seminars/#wednesday">The Wednesday Seminar, University
of Cambridge</a>, 27 Jan 2010.</li>

<li><i>Graphical reasoning in symmetric monoidal categories</i>. Lucas Dixon. Invited talk at University of Leicester, 5
Nov 2009 [<a href="http://dream.inf.ed.ac.uk/projects/quantomatic/talks/gralog-leicester-mongraphs-09-2x2.pdf">pdf</a>]</li>

<li><i>Monoidal Theories and Graph Rewriting in Quantum Computing</i>. Aleks Kissenger and Lucas Dixon. At CAM-CAD, 17 Oct
2009 [<a href="http://dream.inf.ed.ac.uk/projects/quantomatic/talks/camcad_pres-09.pdf">pdf</a>]</li>

<li><i>Quantum CS with Graph Rewriting and CAS</i>. Aleks Kissenger. Calculemus, 6 Jul 2009 [<a href="http://dream.inf.ed.ac.uk/projects/quantomatic/talks/calculemus-09.pdf">pdf</a>]</li>

</ul>