Non-Invertible symmetries of stabilizer codes: towards robust topological quantum memory

We introduce new variants of seminal lattice models in topological quantum information. First, we demonstrate that novel non-invertible transformations (interpretable as generalized symmetries) can map arbitrary classical spin systems in any spatial dimension to dual two-dimensional quantum stabilizer codes. Next, we show that all such non-invertible transformations can be understood as extensions of conventional unitary and anti-unitary maps, emerging naturally as quantum symmetries.

This mapping framework yields models with rich phenomenology, including nontrivial and nonlocal excitations as well as slow dynamical modes that may enable long-lived quantum memories. The thermal coupling between topological charge and low-energy excitations proves significantly more intricate than in standard stabilizer codes. Moreover, this framework offers a broad range of tunable behaviors, encompassing new realizations of topological quantum spin-glass order.