# David Reutter

** David Reutter **

**E:**david.reutter(at)cs.ox.ac.uk

Room 204, Wolfson Building, Parks Road, Oxford OX1 3QD

## Interests

I'm mainly interested in higher category theory and its applications to physics such as in topological quantum field theories or (higher) categorical quantum mechanics.

I'm currently investigating relations between the operator algebraic theory of subfactors, quantum information theory and topological quantum field theories. Most of my work is centered around the concept of `biunitary connections', which are central tools in the study and classification of subfactors. At the same time, several important quantum informatic quantities such as Hadamard matrices and unitary error bases can be expressed as special cases of biunitaries.

## Past

**March 2018.**Invited talk "Quantum functions and the Morita theory of quantum graph isomorphisms" at the workshop Combining viewpoints in quantum theory at the ICMS Edinburgh. A video of the talk can be found here.

**January 2018.**New preprint "The Morita theory of quantum graph isomorphisms" (with Benjamin Musto and Dominic Verdon). We classify instances of quantum pseudo-telepathy in the graph isomorphism game by showing that graphs quantum isomorphic to a graph G correspond to certain Frobenius algebras in a monoidal category of quantum graph automorphisms of G.

**November 2017.**New preprint "A compositional approach to quantum functions" (with Benjamin Musto and Dominic Verdon), describing a 2-categorical approach to finite quantum set and quantum graph theory.

**August 2017.**Invited talk "Frobenius algebras, Hopf algebras and 3-categories" at the conference Hopf algebras in Kitaev's quantum double models at the Perimeter Institute, Canada. A video of my talk can be found here.

**July 2017.**New preprint "A classical groupoid model for quantum networks" (with Jamie Vicary). We describe a new combinatorial 2-category and use it to model a classical network architecture allowing the execution of several quantum-like tasks such as teleportation, dense coding and secure key distribution.

**July 2017.**Contributed talks "Biunitary constructions in quantum information" and "Shaded tangles for the design and verification of quantum programs" at QPL 2017. Videos of my talks can be found here and here.

**June 2017.**Contributed talks "A 2-categorical approach to composing quantum structures" and "A classical groupoid model for quantum networks" at CALCO 2017. Slides can be found here.

**May & June 2017.**Public workshop "Build your own quantum computer" at the Hay festival and the Cheltenham science festival (with Jamie Vicary).

**January 2017.**Contributed talk "Biunitary constructions in quantum information" at QIP 2017, the top international quantum information conference. Slides and video of the talk can be found here and here.

**January 2017.**New preprint "Shaded tangles for the design and verification of quantum programs" (with Jamie Vicary). We give a tangle-based graphical language for the description of quantum circuits such that isotopic tangles yield equivalent programs. This leads to several new protocols and topological insight into known phenomena such as error correcting codes and local inversion of cluster states.

**September 2016.**Jamie Vicary and I have recently written a paper, titled "Biunitary constructions in quantum information", in which we use the interpretation of Hadamard matrices, unitary error bases and quantum Latin squares as biunitaries to obtain many new construction methods for these quantities. An extended abstract can be found here.

## Biography

From 2010 to 2014, I did a Bachelor's and Master's degree in physics at ETH Zürich, mainly focussing on mathematical physics and geometry. In Zürich, I wrote a semester thesis on mutual information quantities associated to a generalized quantum entropy and a master's thesis on geometric constructions of conformal blocks. I then went on to do Part III in mathematics at the University of Cambridge where I wrote an essay on the Atiyah-Singer index theorem and got interested in category theory and its applications to physics.