My work is on higher category theory and its applications in computer science and mathematics, particularly in areas related to quantum structures.
- 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.
- August 2016. Contributed talk "Semistrict 4-categories and strong adjunctions", Category Theory 2016, Dalhousie University, Halifax, Canada.
- August 2016. Invited public lecture "Our quantum future" at the University of Dalhousie, Halifax, Canada.
- June 2016. Invited tutorial "An Introduction to Globular ", Foundational Methods in Computer Science , University of British Columbia, Vancouver, Canada.
- May 2016. Invited talk "Formalizing Geometrical Proofs", Georgia Topology Conference , University of Georgia, Athens, USA.
- April 2016. Invited talk "Biunitarity for Quantum Structures", Eighth Workshop on Information and Processes , Fontainebleau, France.
- April 2016. Invited talk "Surface Proofs for Linear Logic", Theoretical Computer Science seminar series, University of Bath, UK.
- March 2016. Invited talk "Unspeakable Cryptography", presented at the First Oxford Cryptography Day , University of Oxford, UK.
- October 2015. Invited talk "Higher Categories and Quantum Computation", presented at Higher TQFT and CQM , Erwin Scrödinger Institute, Vienna, Austria.
- July 2015. Contributed talk "Automated Higher Rewriting", presented at Higher Dimensional Rewriting and its Applications , Warsaw, Poland.
- June 2015. Invited talk "Higher Categories and Quantum Field Theories", presented at the 18th Symposium on Topological Quantum Information , Athens, Greece.
- June 2015. Invited talk "Topological Foundations for Computation", presented at Low-Dimensional Topology and its Relationships with Physics , AMS-EMS-SPM Joint International Meeting, Porto, Portugal.
- April 2015. Invited talk at Workshop on Homotopy Type Theory and Physics, University of Bristol, UK.
Here's some other things I'm doing at the moment.
- I co-organize the Oxford Advanced Seminar in Informatic Structures (OASIS), with Chris Heunen, Clare 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.
Groupoid Semantics for Thermal Computing
Krzysztof Bar and Jamie Vicary
Wormholes and entanglement
John Baez and Jamie Vicary
Topological Structure of Quantum Algorithms
In Proceedings of the 28th Annual ACM/IEEE Symposium on Logic in Computer Science. Pages 35. 2013.