The four-qubit code is encoded on qubits with even indices and the other qubits are used to make the fault-tolerant parity measurement. The circuit measures S X by setting U=1 and S Z by setting U = H , where H is the Hadamard gate. The circuit measures W if we set U = T . The measurement outcome M gives the reading of the parity measurement. Essential to the fault-tolerant procedure are flag fault-tolerant readout circuits 4 , 5 , 27 , 51 that identify errors that occur during the parity measurement. Outcomes f and g are flag qubit readings that indicate that the circuit may have introduced a logical error to the data qubits.
