Fig. 3. Example Pauli propagation.
Two examples of Pauli propagation through the flagged measurement circuit for a Z-gauge operator. Pauli Z corrections due to deflagging are shown in dotted boxes and depend on the flag qubit measurement results. In the lower half of the figure in blue, a cx gate is followed by a XY error (blue) with probability pcx/15. The subsequent cx gate propagates the X error to the syndrome qubit Q19, flipping the measurement m, and meanwhile the Y error on Q2 propagates without change (it will have an effect on future measurement rounds). The propagated errors are in dotted circles. Note the flag measurement b is not flipped, as the Hadamard gate takes the X error to a harmless Z error. In the top half of the figure, a Pauli Z error occurs on a flag qubit (red) with probability pcx/15, and propagates to a Z error on Q6 and an X error before the measurement a (dashed circles). Deflagging applies Z to Q6, canceling the error there, so that the final propagated error is just the flip of measurement a.