Author(s): Arman Sauliere, Guglielmo Lami, Pedro Ribeiro, Andrea De Luca, and Jacopo De Nardis We study error-correction protocols in which a quantum channel encodes logical information into an enlarged Hilbert space through a one-dimensional random circuit with local gates. We consider both noise acting after the encoding step and noise affecting the encoding circuit itself. Using the cohere… [Phys. Rev. Lett. 137, 120402] Published Wed Sep 16, 2026