Théorique, numérique
Imposing symmetries (say, translation invariance) on quantum systems usually messes up the ability to compose them together meaningfully; for example, imposing translation invariance on systems A and B is usually not the same thing as imposing it on system AB as a whole. The goal of the internship is to build a framework that would resolve this compositionality issue, by building upon the recently introduced framework of routed quantum circuits, which is apt for the description of systems that feature particular symmetries. A promising area of application of these methods is the field of quantum reference frames, which asks the question of what it would mean to describe the world from the perspective of a (potentially superposed) quantum system. In quantum reference frames, one is faced with a "paradox of the third particle", showing that adding new objects to the description leads to paradoxical effects. This is an avatar of the tension between compositionality and the symmetries imposed to model quantum reference frames. The other goal of the internship is therefore to apply the general framework developed to a resolution of this paradox.