Publications

Piecewise Boolean algebras and their domains
Chris Heunen
In 41st International Colloquium on Automata‚ Logic‚ and Programming. Vol. 8573 of Lecture Notes in Computer Science. Pages 208−219. Springer. 2014.
Details about Piecewise Boolean algebras and their domains  BibTeX data for Piecewise Boolean algebras and their domains  DOI (10.1007/9783662439517_18)

Compositional quantum logic
Bob Coecke‚ Chris Heunen and Aleks Kissinger
In Bob Coecke‚ Luke Ong and Prakash Panangaden, editors, Computation‚ Logic‚ Games‚ and Quantum Foundations. Chapter Compositional Quantum Logic. Pages 21−36. 2013.
Details about Compositional quantum logic  BibTeX data for Compositional quantum logic  DOI (10.1007/9783642381645_3)  Link to Compositional quantum logic

Category−Theoretic Quantitative Compositional Distributional Models of Natural Language Semantics
Edward Grefenstette
PhD Thesis June, 2013.
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A new description of orthogonal bases
Bob Coecke‚ Dusko Pavlovic and Jamie Vicary
In Electronic Notes in Theoretical Computer Science. Vol. 23. No. 3. Pages 555–567. 2013.
Details about A new description of orthogonal bases  BibTeX data for A new description of orthogonal bases  DOI (http://dx.doi.org/10.1017/S0960129512000047)  Link to A new description of orthogonal bases

Noncommutativity as a colimit
Benno van den Berg and Chris Heunen
In Applied Categorical Structures. Vol. 20. No. 4. Pages 393−414. 2012.
Details about Noncommutativity as a colimit  BibTeX data for Noncommutativity as a colimit  DOI (10.1007/s1048501192463)

Relative Frobenius algebras are groupoids
Chris Heunen‚ Ivan Contreras and Alberto S. Cattaneo
In Journal of Pure and Applied Algebra. Vol. 217. Pages 114−124. 2012.
Details about Relative Frobenius algebras are groupoids  BibTeX data for Relative Frobenius algebras are groupoids  DOI (10.1016/j.jpaa.2012.04.002)  Link to Relative Frobenius algebras are groupoids

The order encoding: from tractable CSP to tractable SAT
Justyna Petke and Peter Jeavons
No. RR−11−04. DCS‚ University of Oxford. 2011.
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Categorical Tensor Network States
Stephen R.Clark Jacob D. Biamonte and Dieter Jaksch
No. RR−10−14. OUCL. September, 2010.
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Towards quantum chemistry on a quantum computer
A. Aspuru−Guzik Guzik & A. G. White B. P. Lanyon J. D. Whitfield G. G. Gillett M. E. Goggin M. P. Almeida I. Kassal J. D. Biamonte (Oxford) B. J. Powell M. Barbieri
In Nature Chem.. No. 2. Pages 106–111. 2010.
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Categorical properties of the complex numbers
Jamie Vicary
In Journal of Mathematical Physics. 2010.
To appear
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Categorical formulation of finite−dimensional quantum algebras
Jamie Vicary
In Communications in Mathematical Physics. 2010.
To appear
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Generalised Proof−Nets for Compact Categories with Biproducts
Ross Duncan
In S. Gay and I. Mackie, editors, Semantics of Quantum Computation. Cambridge University Press. 2009.
Preprint available at http://arxiv.org/abs/0903.5154
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Graph States and the necessity of Euler Decomposition
Ross Duncan and Simon Perdrix
In K. Ambos−Spies‚ B. Löwe and W. Merkle, editors, Computability in Europe: Mathematical Theory and Computational Practice (CiE'09). Vol. 5635 of Lecture Notes in Computer Science. Pages 167–177. Springer. 2009.
Preprint available at http://arxiv.org/abs/0902.0500
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Graphical Reasoning in Compact Closed Categories for Quantum Computation
Lucas Dixon and Ross Duncan
In Annals of Mathematics and Artificial Intelligence. 2009.
preprint available at http://arxiv.org/abs/0902.0514
Details about Graphical Reasoning in Compact Closed Categories for Quantum Computation  BibTeX data for Graphical Reasoning in Compact Closed Categories for Quantum Computation  Download (pdf) of Graphical Reasoning in Compact Closed Categories for Quantum Computation  DOI (10.1007/s104720099141x)

The Group Theoretic Origin of Non−Locality For Qubits
Bob Coecke‚ Bill Edwards and Rob Spekkens
No. RR−09−04. OUCL. 2009.
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Realizable Hamiltonians for universal adiabatic quantum computers
J.D. Biamonte and Peter J. Love
In Physical Review A 78‚ 012352. 2008.
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Extending Graphical Representations for Compact Closed Categories with Applications to Symbolic Quantum Computation
Lucas Dixon and Ross Duncan
In Serge Autexier‚ John Campbell‚ Julio Rubio‚ Volker Sorge‚ Masakazu Suzuki and Freek Wiedijk, editors, Intelligent Computer Mathematics‚ 9th International Conference‚ AISC 2008‚ 15th Symposium‚ Calculemus 2008‚ 7th International Conference‚ MKM 2008‚ Birmingham‚ UK‚ July 28 − August 1‚ 2008. Proceedings. Vol. 5144 of Lecture Notes in Computer Science. Pages 77−92. Springer. 2008.
Details about Extending Graphical Representations for Compact Closed Categories with Applications to Symbolic Quantum Computation  BibTeX data for Extending Graphical Representations for Compact Closed Categories with Applications to Symbolic Quantum Computation  Download of Extending Graphical Representations for Compact Closed Categories with Applications to Symbolic Quantum Computation  DOI (10.1007/9783540851103_8)

Interacting Quantum Observables
Bob Coecke and Ross Duncan
In Automata‚ Languages and Programming‚ 35th International Colloquium‚ ICALP 2008‚ Reykjavik‚ Iceland‚ July 7−11‚ 2008‚ Proceedings‚ Part II. Vol. 5126 of Lecture Notes in Computer Science. Pages 298−310. Springer. 2008.
A significantly revised and expanded version of this paper is available as preprint http://arxiv.org/abs/0906.4725
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Non−perturbative k−body to two−body commuting conversion Hamiltonians and embedding problem instances into Ising spins
J.D. Biamonte
In Physical Review A 77‚ 052331. 2008.
Details about Non−perturbative k−body to two−body commuting conversion Hamiltonians and embedding problem instances into Ising spins  BibTeX data for Non−perturbative k−body to two−body commuting conversion Hamiltonians and embedding problem instances into Ising spins  Download of Non−perturbative k−body to two−body commuting conversion Hamiltonians and embedding problem instances into Ising spins  DOI (10.1103/PhysRevA.77.052331)  Link to Non−perturbative k−body to two−body commuting conversion Hamiltonians and embedding problem instances into Ising spins

Scalar Inverses in Quantum Structuralism
Bob Coecke and Dusko Pavlovic
No. RR−08−03. OUCL. 2008.
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Classical and Quantum Structures
Bob Coecke‚ Eric O Paquette and Dusko Pavlovic
No. RR−08−02. OUCL. 2008.
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A categorical framework for the quantum harmonic oscillator
Jamie Vicary
In International Journal of Theoretical Physics. Vol. 47. No. 12. Pages 3408–3447. 2008.
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Sign and magnitude tunable coupler for superconducting flux qubits
R. Harris et al.
In Physical Review Letters 98‚ 177001. 2007.
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Complete Positivity without Positivity and Without Compactness
Bob Coecke
No. RR−07−05. Oxford University Computing Laboratory. September, 2007.
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Deciding Bit−Vector Arithmetic with Abstraction
Randal E. Bryant‚ Daniel Kroening‚ Joel Ouaknine‚ Sanjit A. Seshia‚ Ofer Strichman and Bryan Brady
In Proceedings of TACAS 2007. Vol. 4424 of Lecture Notes in Computer Science. Pages 358–372. Springer. 2007.
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Verification of Boolean Programs with Unbounded Thread Creation
Byron Cook‚ Daniel Kroening and Natasha Sharygina
In Theoretical Computer Science (TCS). Vol. 388. Pages 227–242. 2007.
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Symbolic Backwards Reachability Analysis for Higher−Order Pushdown Systems
M. Hague and C.−H. L. Ong
In FoSSaCS. 2007.
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Types for Quantum Computing
Ross Duncan
PhD Thesis 2006.
This thesis was the runner up for the British Computer Society Distinguished Dissertation award.
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A Categorical Quantum Logic
Samson Abramsky and Ross Duncan
In Mathematical Structures in Computer Science. Vol. 16. No. 3. Pages 469−489. 2006.
Preprint available at http://arxiv.org/abs/quant−ph/0512114
Details about A Categorical Quantum Logic  BibTeX data for A Categorical Quantum Logic  Download (pdf) of A Categorical Quantum Logic  DOI (10.1017/S0960129506005275)

Quantum measurements without sums
Bob Coecke and Dusko Pavlovic
No. RR−06−02. Oxford University Computing Laboratory. July, 2006.
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From Separation Logic to First−Order Logic
P. Gardner C. Calcagno and M. Hague
In FoSSaCS. 2005.
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Believe it or not‚ Bell states are a model of multiplicative linear logic
Ross Duncan
No. RR−04−18. Oxford University Computing Laboratory. October, 2004.
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A Categorical Quantum Logic
Samson Abramsky and Ross Duncan
In Proceedings of the 2nd International Workshop on Quantum Programming Languages. Vol. 33 of Turku Centre for Computer Science General Publication. 2004.
This paper is largely superceded by the MSCS publication with the same title‚ however some details‚ such as the sequent calculus presentation‚ are only found in this version.
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A Categorical semantics of Quantum Protocols
Samson Abramsky and Bob Coecke
No. RR−04−02. Oxford University Computing Laboratory. February, 2004.
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Static Checkers for Tree Structures and Heaps
M. Hague
Master's Thesis Imperial College London. 2004.
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The Logic of Entanglement. An invitation. (Version 0.9999)
Bob Coecke
No. RR−03−12. Oxford University Computing Laboratory. October, 2003.
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