Braiding for the win: Harnessing braiding statistics in topological states to win quantum games

Nonlocal quantum games provide proof-of-principle that quantum resources can confer advantage at certain tasks. They also provide a compelling way to explore the computational utility of phases of matter on quantum hardware. In a recent manuscript [arXiv:2403.04829] we demonstrated that a toric code resource state conferred advantage at a certain nonlocal game, which remained robust to small deformations of the resource state. In this talk, I will demonstrate that this robust advantage is a generic property of resource states drawn from topological or fracton ordered phases of quantum matter. The key in every case is to construct a nonlocal game that harnesses the characteristic braiding processes of the quantum phase as a source of contextuality. I will also relate the operators to be measured to order and disorder parameters of an underlying generalized symmetry-breaking phase transition, and massively generalize the family of games that admit perfect strategies when codewords of homological quantum error-correcting codes are used as resources.