  Active error decoding and correction of topological quantum codes - in
particular the toric code - remains one of the most viable routes to large
scale quantum information processing. In contrast, passive error correction
relies on the natural physical dynamics of a system to protect encoded quantum
information. However, the search is ongoing for a completely satisfactory
passive scheme applicable to locally-interacting two-dimensional systems. Here,
we investigate dynamical decoders that provide passive error correction by
embedding the decoding process into local dynamics. We propose a specific
discrete time cellular-automaton decoder in the fault tolerant setting and
provide numerical evidence showing that the logical qubit has a survival time
extended by several orders of magnitude over that of a bare unencoded qubit. We
stress that (asynchronous) dynamical decoding gives rise to a Markovian
dissipative process. We hence equate cellular-automaton decoding to a fully
dissipative topological quantum memory, which removes errors continuously. In
this sense, uncontrolled and unwanted local noise can be corrected for by a
controlled local dissipative process. We analyze the required resources,
commenting on additional polylogarithmic factors beyond those incurred by an
ideal constant resource dynamical decoder.
