  Quantum-enhanced measurements hold the promise to improve high-precision
sensing ranging from the definition of time standards to the determination of
fundamental constants of nature. However, quantum sensors lose their
sensitivity in the presence of noise. To protect them, the use of quantum error
correcting codes has been proposed. Trapped ions are an excellent technological
platform for both quantum sensing and quantum error correction. Here we present
a quantum error correction scheme that harnesses dissipation to stabilize a
trapped-ion qubit. In our approach, always-on couplings to an engineered
environment protect the qubit against spin- or phase flips. Our dissipative
error correction scheme operates in a fully autonomous manner without the need
to perform measurements or feedback operations. We show that the resulting
enhanced coherence time translates into a significantly enhanced precision for
quantum measurements. Our work constitutes a stepping stone towards the
paradigm of self-correcting quantum information processing.
