error correction may identify which error occurred. Consider an $IZ$ error on the second CNOT, in the non-flag circuit this would result in a weight two error, but in this case, this fault causes the circuit to flag. (c) An alternative flag circuit with lower depth than (b). All bad locations are illustrated in blue.[]{data-label="fig:ErrorPropSteane"}](StabNonFT.png "fig:"){width="\textwidth"}

[0.3]{} ![Circuits for measuring the operator $ZZZZ$ (can be converted to any Pauli by single qubit Cliffords). (a) Non-fault-tolerant circuit. A single fault $IZ$ occurring on the third CNOT (from the left) results in the error $IIZZ$ on the data block. (b) Flag version of \[fig:StabNonFT\]. An ancilla (flag) qubit prepared in ${|+\rangle}$ and two extra CNOT gates signals when a weight two data error is caused by a single fault. Subsequent rounds of error correction may identify which error occurred. Consider an $IZ$ error on the second CNOT, in the non-flag circuit this would result in a weight two error, but in this case, this fault causes the circuit to flag. (c) An alternative flag circuit with lower depth than (b). All bad locations are illustrated in blue.[]{data-label="fig:ErrorPropSteane"}](Weight4Generator.png "fig:"){width="\textwidth"}

[0.25]{} ![Circuits for measuring the operator $ZZZZ$ (can be converted to any Pauli by 