Table 1 Probability distributions (in percentage) of measured logical states |*L*_{a}*L*_{b}〉 for various prepared logical states in each row, with and without stabilizers *S*_{x} or *S*_{z} applied.The measurement basis is shown in the last column. The logical states are |00 > _{L} … |11 > _{L}, measured in the *Z*-basis, and | + + 〉_{L} … | − − 〉_{L}, measured in the *X*-basis. The very low error probability on the first logical qubit *L*_{a} compared to *L*_{b} shows the action of its fault-tolerant construction. We run every circuit 5000 to 6000 times. The results without stabilizer show the number of rejected runs from the parity check on the data qubits (typically ~8%) whereas the additional discard on the results with stabilizer (typically ~20%) is due to the ancilla result. The physical errors for state preparation and measurement are 0.3(1)% for states |0〉 and | + 〉, and 1.2(1)% for states |1〉 and | − 〉.