Quantum states can quickly decohere due to their interaction with the environment and imperfections in the applied quantum controls. Quantum error correction promises to preserve coherence by encoding the state of each qubit into a multi-qubit 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.

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.

Our work demonstrates that, at the current gate error levels, using tailored codes with more qubits can be advantageous for error-correction.

Reference:  S. Huang, K. R. Brown and Marko Cetina

https://arxiv.org/abs/2312.10851