Our main themes of research
Diagrammatic Calculi, such as the ZX-calculus and the GHZ/W-calculus, can be used as an alternative to the traditional Hilbert Space formalism in order to study quantum computation and information. This theme of research is concerned with the development, extension and applications of such calculi.
Quantum foundations aims to understand why quantum mechanics is the way it is, whether our current mathematical treatment of quantum theory is the best description, what can be done in a quantum world, and, whether we can find any extensions to quantum mechanics for example leading to a theory of quantum gravity.
This area of research is concerned with the development of formal methods and software tools which can be used for automated reasoning about diagrammatic theories based on String Diagrams (e.g. ZX-calculus, GHZ/W calculus).
Categorical models for quantum mechanics are generalisations of Hilbert spaces, which preserves only those features that are essential for quantum information. This framework comes with a diagramatic counterpart, which makes it easy to reason about quantum protocols and verify their correctness.
We use the general setting of process theories to reason abstractly about the structure of quantum algorithms. This theme involves the characterization of quantum algorithms, especially the structures that lead to speedups, and the search for new algorithms.
Both the pregroups of Lambek for modelling language structure, and the category of real vector spaces in which distributional models of meaning are constructed are compact monoidal categories. This observation connects sentence structure and vector space models, opening up the possibility of a compositional theory of meaning.