Measuring Non-Zero Syndromes

Quantum error correction codes are designed to identify and locate errors such that they can be properly corrected by recovery operations. Here, we demonstrate that, in realistic error environments, if a syndrome measurement indicates an error has occurred the assumed recovery will not, in general, lead to a corrected state. The efficacy of the recovery operation properly depends on the likelihood of different error types, the relative probability an error may have occurred at strategic points during the error correction process itself, and on the error correlations between the qubits taking part in a two qubit gate.