The Knill-Laflamme condition is sufficient for the autonomous protection of logical qudits by strong engineered dissipation. (arXiv:1711.02999v2 [quant-ph] UPDATED)

Autonomous quantum error correction utilizes the engineered coupling of a
quantum system to a dissipative ancilla to protect quantum logical states from
decoherence. We show that the Knill-Laflamme condition, stating that the
environmental error operators should act trivially on a subspace, which then
becomes the code subspace, is sufficient for logical qudits to be protected
against Markovian noise. It is proven that the error caused by the total
Lindbladian evolution in the code subspace can be suppressed up to very long
times in the limit of large engineered dissipation, by explicitly deriving how
the error scales with both time and engineered dissipation strength. To
demonstrate the potential of our approach for applications, we implement our
general theory with binomial codes, a class of bosonic error-correcting code,
and outline how they can be implemented in a fully autonomous manner to protect
against photon loss and dephasing errors in a microwave cavity.

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