  Quantum states can quickly decohere through interaction with the environment.
Quantum error correction is a method for preserving coherence through active
feedback. Quantum error correction encodes the quantum information into a
logical state with a high-degree of symmetry. Perturbations are first detected
by measuring the symmetries of the quantum state and then corrected by applying
a set of gates based on the measurements. In order to measure the symmetries
without perturbing the data, ancillary quantum states are required. Shor error
correction uses a separate quantum state for the measurement of each symmetry.
Steane error correction maps the perturbations onto a logical ancilla qubit,
which is then measured to check several symmetries simultaneously. Here we
experimentally compare Shor and Steane correction of bit flip errors using the
Bacon-Shor code implemented in a chain of 23 trapped atomic ions. We find that
the Steane error correction provides better logical error rates after a
single-round of error correction and less disturbance to the data qubits
without error correction.
