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.
Here are some things I've been working on recently:
- Ben Musto and have a new paper on the arXiv on quantum Latin squares, which are quantum generalizations of ordinary Latin squares. We show how you can use them to make completely new sorts of teleportation protocol.
- Topological quantum field theory (TQFT) is a simple type of quantum field theory in which diffeomorphic manifolds are assigned equivalent invariants. Bruce Bartlett, Chris Douglas, Chris Schommer-Pries and I are working on a family of results that give a complete classification of once-extended 3-dimensional TQFTs, in a categorical style, and the first paper is now up on the arXiv.
- 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.
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'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 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.
- Since 2012, I've been lecturing a course on Categorical Quantum Mechanics with my colleague Chris Heunen, and we're also writing a book that will come out soon with OUP.
- 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.
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.