Webpage of the Compositional Systems and Methods group at TalTech.

A graphical calculus for Lagrangian relations

Symplectic vector spaces can be interpreted as the phase space of configurations of linear mechanical systems. The category of linear/affine Lagrangian relations between symplectic vector spaces is a symmetric monoidal subcategory of relations which gives a semantics for the evolution -- and more generally linear/affine constraints on the evolution -- of the phase space of these mechanical systems.

In this work, we give a complete string diagrammatic presentation of the category of linear/affine Lagrangian relations in terms of a `doubled' category of linear/affine relations.

I will talk about how this gives a string-diagrammatic semantics for electrical circuits, or stabilizer quantum circuits depending on the interests of the members of the audience.

This is joint work with Aleks Kissinger. URL: https://arxiv.org/abs/2105.06244