Fractons, Strange Correlators and Dualities via Cluster State Measurements

The Calderbank-Shor-Steane (CSS) code is a class of quantum error correction codes that contains the toric code and fracton models. We use the chain complex representation of CSS codes to arrive at a web of dualities that generalizes the Wegner's duality in generalized quantum Ising models. Further, we provide a procedure to obtain statistical models associated with a given CSS code via the foliated cluster state, and derive a generalization of the Kramers-Wannier-Wegner duality for such statistical models. Moreover, we give a measurement-assisted gauging method with cluster-state entanglers for CSS/fracton models, extending results in the literature. We analyze the non-invertible fusion of the Kramers-Wannier transformation operators underpinning the gauging procedure. The cluster-state entanglers also allow us to construct a generalization of the notion of strange correlators to fracton models.