Senior Research Fellow
Room 213, Wolfson Building, Parks Road, Oxford OX1 3QD
My work is on high-level mathematical structures for fundamental phenomena in computer science and physics. There is a lot in common between these fields, which both study the laws and emergent features of systems with local interactions. Particular areas of recent interest include the structure of quantum algorithms, a new higher-categorical language for physics and computer science, and the classification of topological quantum field theories.
I hold a Senior Research Fellowship at the Quantum Group in the Computer Science department of the University of Oxford, and also a Research Fellowship at the Centre for Quantum Technologies at the National University of Singapore. I am also a Research Fellow at Wolfson College, Oxford.
Here are summaries of some recent results:
- Recent work on quantum algorithms uses a topological formalism to give a new description of the Deutsch-Jozsa, single-shot Grover and hidden subgroup algorithms. This high-level approach gives rise to new proofs of correctness, and new 'multicoloured' quantum search procedures which are more powerful than the traditional Grover algorithm and its existing generalizations. This work was presented at LICS 2013, and a paper is available.
- I've been working on a higher-categorical theory of information flow, which uses topological diagrams involving points, lines and surfaces to represent informatic procedures such as encryption, quantum measurement and controlled operations. Equations between diagrams specify procedures such as quantum teleportation and encrypted communication, and solutions to these equations in monoidal bicategories correspond to real-world implementations of the procedures. Some of this work was presented at LICS 2012 and MFPS 2013. Papers are available here and here. Some of this research is joint work with Mike Stay.
- Topological quantum field theory (TQFT) is a simple type of quantum field theory in which only the topology of a manifold is recognized. These theories have no issues with divergences, yet are rich enough to have a beautiful mathematical theory, which is still not fully understood. They are also the basis for topological quantum computation, an important model of quantum computing. With Bruce Bartlett, Chris Douglas and Chris Schommer-Pries I am working on a family of results that give for the first time a complete classification of once-extended 3-dimensional TQFTs.
If you're interested in these ideas, please get in touch! I am always interested in giving talks, meeting other scientists with similar interests and starting new collaborations.
Here are some places I'm planning to be:
- October 17: Giving a talk at the Imperial College LogIC seminar series: "A Geometrical Logic for Information Flow"
- December 15-18 2013: Going to the Workshop on Informatic Phenomena 2013.
- March 24-28 2014: Going to a Banff workshop in low-dimensional topology
Here's some other things I'm doing at the moment:
- I'm a coordinator for CAP, an EPSRC-funded research network that supports travel for conferences and collaboration for research in the intersection of Computer Science and Physics. If you'd like to apply for funding, please get in touch.
- I co-organize the Oxford Advanced Seminar in Informatic Structures (OASIS), with Chris Heunen and Clare Horsman.
- 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 800 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 wrote a lecture course on Categorical Quantum Mechanics with my colleague Chris Heunen. We lectured this in 2012 and 2013, and will give the course again in 2014.
- I will be lecturing the Lambda Calculus and Types course for 3rd year undergraduates and Masters students in this coming academic year.
- I frequently supervise DPhil, MSc and undergraduate students (and sometimes school students too!) on topics related to the mathematical foundations of quantum computing. If you'd like to work on a project with me, get in touch.
The Topology of Quantum Algorithms
Pages 35. 2912.
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.
The Categorified Heisenberg Algebra I: A Combinatorial Representation
Jeffrey C. Morton and Jamie Vicary
Pages 29. 2012.