My work focuses on applying algebraic and categorical structures to problems in quantum information theory.
1. Reference frame independent quantum teleportation without prior alignment.
We propose schemes for quantum teleportation between parties whose reference frames are misaligned by the action of a compact Lie group. These schemes do not require prior alignment or the use of decoherence-free subspaces, and are robust against changes in reference frame alignment during execution. They utilise algebraic structures called equivariant unitary error bases, which we completely classify for qubits.
- Perfect tight quantum teleportation without a shared reference frame (with Jamie Vicary)
Phys. Rev. A 98, 012306. doi: 10.1103/PhysRevA.98.012306
- Quantum teleportation with infinite reference frame uncertainty and without prior alignment (with Jamie Vicary)
Submitted for publication
A very early version of this work appeared at QPL2016:
- Tight reference frame-independent quantum teleportation (with Jamie Vicary)
Quantum Physics and Logic 2016, EPTCS, 236:202-214, 2017. doi: 10.4204/EPTCS.236.13
2. Quantum pseudo-telepathy
We develop a compositional theory of quantum functions using tools from algebra and higher category theory. We apply this to the study of quantum graph isomorphisms, which are perfect quantum strategies for a certain nonlocal game; in particular, we fully classify graphs quantum isomorphic to a given graph, and give a construction of quantum graph isomorphisms based on the automorphism group of the source graph.
- A compositional approach to quantum functions (with Benjamin Musto and David Reutter)
Submitted for publication
- The Morita theory of quantum graph isomorphisms (with Benjamin Musto and David Reutter)
To appear in Comm. Math. Phys. (accepted 17/05/2018)
- A group-theoretical construction of quantum graph isomorphisms (with Benjamin Musto and David Reutter)
3. Higher algebra
We develop a diagrammatic calculus which allows us to prove a result regarding certain higher algebraic structures closely related to topological quantum field theory and topological quantum computation.
- Coherence for braided and symmetric pseudomonoids
In preparation, final version expected by mid-July 2018
- July 2017 - Foundations of Quantum Mechanics (Perimeter Institute)
- September 2017 - Higher Dimensional Rewriting and Applications (Oxford) - Coherence for braided and symmetric pseudomonoids
- September 2017 - Peripatetic Seminar on Sheaves and Logic (Leeds) - Coherence for braided and symmetric pseudomonoids
- June 2016 - Quantum Physics and Logic (Strathclyde) - Tight reference frame-independent quantum teleportation
- I have been class tutor and marker for the Categories, Proofs and Processes and Categorical Quantum Mechanics courses here in Oxford.
- I have given outreach presentations about quantum computing at:
- Target Oxbridge, Oxford, UK (age 16-18)
- Radley College Science Fair, Radley, UK (age 14-16)
- University College Computer Science Open Day, Oxford, UK (age 16-18)
- I have been a referee for:
- New Journal of Physics
- Journal of Pure and Applied Algebra
Prior to my doctoral studies, I completed a MMath degree in Mathematical Sciences at the University of Durham, where I gained a 'Rising Star' Research Award and the 4H Project Prize.