Table 1. Probability distributions (in percentage) of measured logical states |L_aL_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 | − 〉.

	Yield	Measured logical state |LaLb〉				Measurement basis
		|00〉	|01〉	|10〉	|11〉	Z
		| + + 〉	| + − 〉	| − + 〉	| − − 〉	X
|00〉L	91.1(4)	98.0(2)	1.7(2)	0.11(6)	0.18(7)	Z
|00〉LSz	77.8(6)	97.8(2)	1.7(2)	0.18(8)	0.3(1)	Z
|00〉LSx	65.2(7)	97.1(3)	2.4(3)	0.2(1)	0.3(1)	Z
| + + 〉L	91.1(4)	95.7(3)	3.9(3)	0.24(8)	0.22(8)	X
| + + 〉LSz	68.2(7)	93.0(5)	4.2(4)	1.3(2)	1.5(2)	X
| + + 〉LSx	72.1(6)	94.3(4)	4.5(4)	0.5(1)	0.7(2)	X
| − 1〉L	90.1(4)	0.22(8)	50.5(8)	0.09(6)	49.2(8)	Z
| − 1〉L	87.0(5)	0.3(1)	0.3(1)	50.4(8)	48.9(8)	X
| − 1〉LSz	79.9(6)	0.15(7)	50.0(8)	0.10(6)	49.8(8)	Z
| − 1〉LSz	75.5(6)	0.4(1)	0.3(1)	50.1(8)	49.2(8)	X
| − 1〉LSx	72.1(6)	0.6(1)	50.2(8)	0.5(1)	48.7(8)	Z
| − 1〉LSx	76.2(5)	0.4(1)	0.4(1)	50.0(7)	49.2(7)	X
|0 + 〉L	93.2(3)	47.4(5)	52.5(5)	0.06(3)	0.05(3)	Z
|0 + 〉L	92.4(4)	50.0(8)	0.04(4)	49.8(8)	0.09(5)	X
|0 + 〉LSz	81.6(6)	48.3(8)	51.4(8)	0.17(8)	0.17(8)	Z
|0 + 〉LSz	68.5(7)	47.1(9)	2.4(3)	47.4(9)	3.1(3)	X
|0 + 〉LSx	72.0(6)	48.3(8)	51.5(8)	0.16(7)	0.12(7)	Z
|0 + 〉LSx	70.9(7)	49.4(9)	0.4(1)	49.7(9)	0.5(1)	X
|11〉LSz	73.3(6)	0.4(1)	0.3(1)	2.8(3)	96.5(3)	Z