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Jamie Vicary

Personal photo - Jamie Vicary

Jamie Vicary

Senior Research Fellow

E: jamie.vicary@cs.ox.ac.uk
T: (01865 6)10775

Room 208, Wolfson Building, Parks Road, Oxford OX1 3QD

Interests

My work is on higher category theory and its applications in computer science and mathematics, particularly in areas related to quantum structures.

The future

The past

  • March 2017. Extended abstract for "Data structures for quasistrict higher categories" (with Krzysztof Bar) accepted for LICS 2017.
  • February 2017. I have been offered an EPSRC Early Career Fellowship.
  • January 2017. New preprint "Shaded tangles for the design and verification of quantum programs" (with David Reutter), describing new techniques for drawing quantum circuits as shaded tangles, so that circuit verification is just knot isotopy. We also give a new state transfer algorithm for a cluster-based quantum computer, give new constructions of error correcting codes based on unitary error bases, and identify surprising topological properties of the quarter-turn about the X-axis on the Bloch sphere.
  • December 2016. Globular has been loaded 10,000 times by 2,500 users!
  • November 2016. Paper on biunitary constructions (with David Reutter) accepted to QIP 2017, the top international quantum computing conference.
  • October 2016. New 112-page preprint "Data structures for quasistrict higher categories" (with Krzysztof Bar) gives the theoretical foundations for our proof assistant Globular , including a new definition of semistrict 4-category.
  • September 2016. New preprint "Biunitary constructions in quantum information" (with David Reutter.) Many new construction methods relating Hadamard matrices, unitary error bases, quantum Latin squares and controlled families, all illustrated with the graphical calculus for 2-categories.
  • August 2016. Public lecture "Our quantum future" at the University of Dalhousie, Halifax, Canada, introducing quantum computers and discussing the possible impact they might have on society.
  • July 2016. Invited lecturer for the  AARMS Summer School , University of Dalhousie, Halifax, Canada. I gave a 30-hour course on Categories, Quantum Computation and Topology to 30 excellent and motivated students, including a big practical component using Globular.
  • June 2016. The paper "The categorified Heisenberg algebra I: a combinatorial representation" (with Jeffrey Morton), describing a combinatorial interpretation of Khovanov's categorification of the Heisenberg algebra, accepted to appear in JPAA.
  • May 2016. New result (with Krzysztof Bar), formalized here: every adjunction in a semistrict 4-category can be promoted to satisfy the butterfly equations.
  • April 2016. Paper "Globular: a proof assistant for higher rewriting" (with Krzysztof Bar and Aleks Kissinger) accepted for FSCD 2016.
  • March 2016. Preprint "Tight reference frame–independent quantum teleportation" (with Dominic Verdon) available online, describing the first zero-overhead procedure for quantum teleportation without a shared reference frame. UPDATE: accepted for conference QPL 2016.
  • March 2016. Semistrict 4-categories are now supported by Globular.
  • January 2016. Preprint "Surface proofs for linear logic" (with Lawrence Dunn) available online, describing a coherence result for Frobenius pseudomonoids and swallowtailators, with applications to proof equivalence for linear logic. UPDATE: different parts of this work accepted for workshops HDRA 2016 and LINEARITY 2016.
  • December 2015. We are excited to announce the launch of  Globular  (with Krzysztof Bar and Aleks Kissinger), a new online proof assistant for higher category theory. UPDATE: Over 6000 views in 6 months since launch, and 236 person-hours of use!
  • November 2015. The proceedings of QPL 2016 (with Chris Heunen and Peter Selinger) are now available.
  • September 2015. Preprint "Modular categories as representations of the 3-dimensional bordism 2-category" (with Bruce Bartlett, Chris Douglas and Chris Schommer-Pries) available online, giving the first full proof that 3-dimensional topological quantum field theories are classified in terms of modular tensor categories.
  • April 2015. Preprint "Quantum Latin squares and unitary error bases" (with Benjamin Musto) now available, which introduces quantum Latin squares and shows how they can be used to construct new sorts of teleportation protocol. UPDATE: accepted for QIP 2016, the top annual quantum information conference. UPDATE: to appear in Quantum Information & Computation.

Talks

[63] (invited) January 2018. 'TBA', Higher Gauge Theory and Quantum Matter, University of Leeds, UK.
[62] (invited) January 2018. 'TBA', Meeting on Intensional and Extensional Models of Computation, National Institute of Informatics, Tokyo, Japan.
[61] (invited) July 2017. 'TBA', Workshop on Hopf Algebras in Kitaev's Quantum Double Models, Perimeter Institute, Waterloo, Canada.
[60] (invited) July 2017. 'TBA', Higher Structures in Lisbon, Instituto Superior Técnico, Lisbon, Portugal.
[59] (invited) July 2017. 'TBA', 14th International Conference on Quantum Physics and Logic, Institute for Computing and Information Sciences (iCIS), Radboud University, Nijmegen, The Netherlands.
[58] (public) June 2017. 'Build Your Own Quantum Computer', Cheltenham Science Festival, Cheltenham Science Festival, Cheltenham, UK.
[57] (public) May 2017. 'Build Your Own Quantum Computer', Hay Festival, Hay-on-Wye, UK.
[56] (invited) April 2017. 'Formalizing Compositional Proofs', Theoretical Computer Science Seminar, Institut de Recherche en Informatique Fondamentale, Paris, France.
[55] (invited) February 2017. 'Globular: A Proof Assistant for Diagrammatic Science', Babbage Departmental Seminar, Computer Laboratory, University of Cambridge, UK.
[54] (invited) February 2017. 'Formal Proof in Higher Category Theory', 10th Yorkshire and Midlands Category Theory Seminar, University of Leicester, UK.
[53] (invited) December 2016. 'Formalizing Compositional Proofs', Compositionality and Logical Structures in Computation, Simons Institute, University of California, Berkeley, USA.
[52] (invited) November 2016. 'Globular: Higher Categories, The Easy Way', Category Theory seminar series, University of Cambridge, UK.
[51] (invited) October 2016. 'Formalizing Compositional Proofs', Theoretical Computer Science Seminar, University of Birmingham, UK.
[50] (invited) (public) August 2016. 'Our Quantum Future', Distinguished Public Lecture Series, University of Dalhousie, Halifax, Canada.
[49] (invited) July 2016. 'Formalizing Geometrical Proofs', Modelling Topological Phases of Matter, University of Leeds, UK.
[48] (invited) July 2016. 'Categories, Quantum Computation and Topology', AARMS Summer School Lectures, University of Dalhousie, Halifax, Canada. 30-hour intensive lecture course
[47] (invited) June 2016. 'Introduction to Globular', Foundational Methods in Computer Science 2016, University of British Colombia, Vancouver, Canada.
[46] (invited) May 2016. 'Formalizing Geometrical Proofs', 2016 Georgia Topology Conference, University of Atlanta, Athens, USA.
[45] (invited) April 2016. 'Surface Proofs for Linear Logic', Theoretical Computer Science Seminar, University of Bath, UK.
[44] (invited) April 2016. 'Biunitarity for Quantum Structures', Eighth Workshop on Information and Processes (WIP 2016), Fontainebleau, France.
[43] (invited) March 2016. 'Unspeakable Cryptography', First Oxford Cryptography Day, University of Oxford, UK.
[42] (invited) October 2015. 'Higher Categories and Quantum Computation', Higher Topological Quantum Field Theory and Categorical Quantum Mechanics, Erwin Schrodinger Institute, Vienna, Austria.
[41] (invited) June 2015. 'Higher Categories and Quantum Field Theories', 18th Symposium on Topological Quantum Information, University of Athens, Greece.
[40] (invited) June 2015. 'Topological Foundations for Computation', AMS-EMS-SPM Joint International Meeting, Unversity of Porto, Portugal.
[39] (invited) April 2015. 'The Categorified Heisenberg Algebra', Workshop on Homotopy Type Theory and Physics, University of Bristol, UK.
[38] (invited) March 2015. 'Higher Categories and Quantum Computation', Pure Mathematics Seminar, University of Leicester, UK.
[37] (invited) October 2014. 'The Topology of Information Flow', European Telecommunications Standards Institute 2nd Quantum-Safe Crypto Workshop, Ottawa, Canada.
[36] (invited) September 2014. 'The Topology of Information Flow', Quantum Foundations Seminar, Waterloo, Canada.
[35] (invited) September 2014. 'State of the Art: Topology of Quantum Algorithms', Post-Quantum Research - Addressing Future Challenges and Directions, Isaac Newton Institute, University of Cambridge, UK.
[34] (invited) June 2014. 'Topological Quantum Field Theory', Theoretical Physics Seminar, Imperial College London, UK.
[33] (invited) June 2014. 'Topological Foundations of Quantum Computation', Theoretical Physics Seminar, University of Leeds, UK.
[32] (invited) May 2014. 'The Geometry of Information Flow', Departmental Seminar, University of Birmingham, UK.
[31] (invited) May 2014. 'Logical Foundations of Classical Encryption and Quantum Teleportation', Workshop on Post Quantum Research - Identifying Future Challenges and Directions, Isaac Newton Institute, University of Cambridge, UK.
[30] (invited) April 2014. 'Topological Foundations of Classical Encryption and Quantum Teleportation', Seminar at the Centre for Quantum Information and Foundations, DAMTP, University of Cambridge, UK.
[29] (invited) April 2014. 'A Geometrical Logic for Classical and Quantum Computation', Computer Science Theory Seminar, Queen Mary University of London, UK.
[28] (invited) March 2014. 'Computation from Higher Representation Theory', Workshop on Parameterized Morse Theory in Low-Dimensional and Symplectic Topology, Banff Research Station, Canada.
[27] (invited) February 2014. 'Classical and Quantum Computing with Higher Algebraic Structures', Topology Seminar, University of Oxford, UK.
[26] (invited) December 2013. 'Geometric Logic of Information Flow', Workshop on Information and Processes (WIP 2013), Centro de Investigación y Adiestramiento Político y Administrativo (CIAPA), University of Costa Rica, San José, Costa Rica.
[25] (invited) October 2013. 'Geometric Logic of Information Flow', Departmental Seminar, University of Oxford, UK.
[24] (invited) October 2013. 'Geometric Logic of Information Flow', LogIC Seminar, Imperial College London, UK.
[23] (invited) September 2013. 'The Geometry of Quantum and Classical Information', Group Seminar, Research Institute for Mathematical Sciences (RIMS), Kyoto, Japan.
[22] (invited) April 2013. 'Bicategorical Foundations for Quantum Information', Group Seminar, Centre for Australian Category Theory, University of Macquarie, Sydney, Australia.
[21] (invited) March 2013. 'The Geometry of Quantum Information', Quantum Information Seminar, University of Nagoya, Japan.
[20] (invited) March 2013. 'Applications of Category Theory to Quantum Physics', Group Seminar, Hokkaido University, Sapporo, Japan.
[19] (invited) January 2013. 'Topological Structure of Quantum Algorithms', Quantum Information Seminar, University of Bristol, UK.
[18] (invited) March 2012. 'A 2-Categorical Formalism for Quantum Information', Oxford Quantum Information Science Workshop, University of Oxford, UK.
[17] (invited) May 2011. '123 TQFTs', Quantum Field Theory seminar series, University of Oxford, UK.
[16] (invited) May 2011. '123 TQFTs', Workshop on Higher Gauge Theory, TQFTs and Categorification, University of Cardiff, UK.
[15] (invited) April 2011. 'A Bicategorical Syntax for Concurrency', Classical and Quantum Information Flow, Bellairs Research Institute, McGill University, Holetown, Barbados.
[14] (invited) February 2011. 'The Category Theory of Quantum Field Theory', Category Theory seminar series, University of Cambridge, UK.
[13] (invited) February 2011. '123 TQFTs', Workshop on Higher Gauge Theory, TQFT and Quantum Gravity, Instituto Superior Técnico, Lisbon, Portugal.
[12] (invited) June 2010. 'Functorial Semantics of Systems, Spaces and Logics', Seminar on the Semantics of Information, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Germany.
[11] (invited) May 2010. 'Introduction to Monoidal Categories and the Graphical Calculus', QICS Spring School on Foundational Structures in Quantum Computation and Information, University of Oxford, UK.
[10] (invited) March 2010. '3D TQFTs as Frobenius Algebras', Workshop on Information Theory, Quantum Mechanics and Security, Bellairs Research Institute, McGill University, Holetown, Barbados.
[9] (invited) January 2010. 'Complex Numbers and Categorical Structures', Theoretical Computer Science seminar series, University of Birmingham, UK.
[8] (invited) October 2009. 'A New Description of Maximally-Entangled Meaasurements', Second Workshop on Informatic Phenomena (WIP 2009), Tulane University, New Orleans, USA.
[7] (invited) June 2009. 'Higher-Dimensional Quantum Mechanics', Categories, Quanta, Concepts, Perimeter Institute, Waterloo, Canada.
[6] (invited) November 2008. 'A Guide to the Dagger-Functor in Quantum Theory', Analytic Topology seminar series, Mathematical Institute, University of Oxford, UK.
[5] (invited) September 2008. 'The Way of the Dagger', Foundational Structures for Quantum Information and Computation, Obergurgl, Austria.
[4] (invited) March 2008. 'Generalizing C*-Algebras', Workshop on Logic, Physics and Quantum Information Theory, Bellairs Research Institute, McGill University, Holetown, Barbados.
[3] (invited) January 2008. 'A Categorical Framework for the Quantum Harmonic Oscillator', First Workshop on Categories, Logic and the Foundations of Physics, Imperial College London, UK.
[2] (invited) August 2007. 'A Categorical Framework for the Quantum Harmonic Oscillator', Workshop on Categorical Quantum Logic, Department of Computer Science, University of Oxford, UK.
[1] (invited) May 2007. 'A Categorical Framework for the Quantum Harmonic Oscillator', Group Seminar, Department of Computer Science, University of Oxford, UK.

Other things

Here's some other things I'm doing at the moment.

  • I co-organize the Oxford Advanced Seminar in Informatic Structures (OASIS), with Chris HeunenClare Horsman, Aleks Kissinger and Sam Staton.
  • I'm part of the Centre for Quantum Mathematics and Computation (QMAC), an interdisciplinary collaboration between the Oxford's Computer Science, Mathematics and Physics departments.
  • I maintain two popular mailing lists, one for international quantum foundations announcements with over 950 subscribers, and another for quantum computing and quantum foundations events taking place in Oxford with around 100 subscribers. Please get in touch if you'd like to be added to either of these.
  • I am the lecturer for Categorical Quantum Mechanics (with Dan Marsden, and originally with Chris Heunen). These notes are being turned into a textbook with OUP, to be published soon.
  • I frequently supervise DPhil, MSc and undergraduate students on topics related to the mathematical foundations of quantum computing. If you'd like to work on a project with me, get in touch.

Biography

I did an undergraduate degree in Physics at Mansfield College, Oxford, followed by the Part III mathematics course at DAMTP and Trinity Hall, Cambridge. I then did a PhD in category theory and the foundations of quantum information with Chris Isham at Imperial College London, which was awarded in 2009. Since then I have been based in Oxford, becoming a Senior Research Fellow in 2013. In the period 2011-2014 I also held a Senior Research Fellow position at the Centre for Quantum Technologies in Singapore.

Selected Publications

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Activities

Current Students

Past Student