Autonomous Global Decoders for Quantum Memories

Autonomous quantum memories provide passive protection of quantum information using engineered dissipation that yields an ``always-on" decoder. We consider a simple theoretical model of universal global autonomous decoders that can be constructed from a wide family of quantum codes. We prove bounds on the logical error rate as a function of the rates of correction and noise. We find that such a model typically require correction rates that scale polynomially with system size to achieve exponential suppression of logical errors. We apply our results to existing quantum codes codes, including the five-qubit code, the toric code, and the binomial code.