Stabilizing topologically ordered steady-states in systems with heralded noise

Realizing topologically non-trivial states on qubit platforms using local dynamics is a highly sought-after goal as they are important resources for quantum computation and quantum error correction. In low dimensions, these states are unstable at finite temperatures which makes it difficult to maintain their order in the presence of generic noise prevalent in these systems. We present a set of local Lindblad models that host steady-state topological phases in the presence of heralded noise that has become relevant in recently developed erasure-qubit platforms. We demonstrate that the classical information about the location of heralded errors can be effectively used to locally confine quantum defects leading to novel topological mixed-states including non-abelian topologically ordered states. The steady-state phases remain stable up to a finite critical noise rate beyond which the topological order is lost.