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Active error decoding and correction of topological quantum codes - inparticular the toric code - remains one of the most viable routes to largescale quantum information processing. In contrast, passive error correctionrelies on the natural physical dynamics of a system to protect encoded quantuminformation. However, the search is ongoing for a completely satisfactorypassive scheme applicable to locally-interacting two-dimensional systems. Here,we investigate dynamical decoders that provide passive error correction byembedding the decoding process into local dynamics. We propose a specificdiscrete time cellular-automaton decoder in the fault tolerant setting andprovide numerical evidence showing that the logical qubit has a survival timeextended by several orders of magnitude over that of a bare unencoded qubit. Westress that (asynchronous) dynamical decoding gives rise to a Markoviandissipative process. We hence equate cellular-automaton decoding to a fullydissipative topological quantum memory, which removes errors continuously. Inthis sense, uncontrolled and unwanted local noise can be corrected for by acontrolled local dissipative process. We analyze the required resources,commenting on additional polylogarithmic factors beyond those incurred by anideal constant resource dynamical decoder.

Cellular automaton decoders of topological quantum memories in the fault tolerant setting