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 a relation between the operator algebraic theory of subfactors and quantum information theory. This relation 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, unitary error bases and quantum Latin squares can be expressed as special cases of biunitaries.
- 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.
- 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.
UPDATE: accepted to QIP 2017, the top international quantum information conference. Slides and video of the talk can be found here and here.
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.