11.9 Turning bit-flips into phase-flips

The three-qubit code that we have just demonstrated is sufficient to protect a qubit against single bit-flips, but not phase-flips. But this is good enough. Recall that HZH=X, and so it is enough to sandwich the decoherence area in between the Hadamard gates: they will turn phase flips into bit flips, and we already know hot to protect our qubits against Z-errors. The encoded state \alpha|0\rangle + \beta|1\rangle now reads \alpha|+++\rangle+\beta|---\rangle, where |\pm\rangle=|0\rangle\pm|1\rangle.