that the output codeword differs from a valid codeword by an error of weight at most one. Note that the above argument applies irrespective of any errors on the input state, hence the second criteria of \[Def:FaultTolerantDef\] is satisfied. It is worth pointing out that up to three repetitions are required in order to guarantee that the second criteria of \[Def:FaultTolerantDef\] is satisfied (unless the code has the property that all states are at most a weight-one error away from a valid codeword, as in [@CR17v1]).

The Steane code is an example which satisfies the Flag $1$-FTEC condition with a simple choice of circuits. To verify this, the representation of the Steane code given in \[fig:SteaneColor1\] is useful. There is an $X$- and a $Z$-type stabilizer generator supported on the four qubits of each of the three faces. First let us specify all six stabilizer measurement circuits. The circuit that measures $Z_{q_1}Z_{q_2}Z_{q_3} Z_{q_4}$ is specified by taking qubits $q_1$, $q_2$, $q_3$, and $q_4$ to be the four data qubits in descending order in the 1-flag circuit in \[fig:StabFTwithAncilla\]. The other two $Z$-stabilizer measurement circuits are obtained by first rotating \[fig:SteaneColor1\] by $120^{\circ}$ and $240^{\circ}$ and then using \[fig:StabFTwithAncilla\]. The $X$-stabilizer 