Anasuya Lyons

Abstract A quantum computer requires the ability to store and manipulate information globally to protect against local noise. Topologically ordered phases1,2 offer two routes: encoding information in the ground-state subspace3 or in anyonic excitations1,4,5. The toric code1 exemplifies the first approach but does not intrinsically support a universal gate set. The latter—topological quantum computation—implements gates by braiding non-Abelian anyons6 around each other.

Abstract We formulate a semiclassical circuit model to clarify the role of quantum entanglement in the recently discovered encoding phase transitions in quantum circuits with measurements. As a starting point, we define a random circuit model with nearest neighbor classical gates interrupted by erasure errors. In analogy with the quantum setting, this system undergoes a purification transition at a critical error rate above which the classical information entropy in the output state vanishes.