thresholds of quantum error correction codes

#Thresholds of quantum error correction codes code

Table 1 (see Materials and Methods) summarizes results for different logical states prepared with the circuits shown in Fig. The opposite is true when applying the stabilizers to |++〉 instead. S z introduces Z-type errors, which do not affect |00〉 L. S x introduces X-type errors in the system, which can be seen from a higher L b error. The errors on L a are 0.2(1)%, similar to the error floor given by the |11〉 L population, which is slightly higher than after mere state preparation due to the additional gates introduced by the stabilizers. The results of the logical states are similar, with |00〉 L populations of 97.8(2) and 97.1(3)%, respectively, and the errors occur predominantly in the non–fault-tolerantly prepared gauge qubit L b. Populations in the odd-numbered states reflect events where an error is detected by a stabilizer. 2 (E and F), for nondemolition syndrome extraction. With |00〉 L thus prepared, we apply in turn the two stabilizers S z and S x, shown in Fig. Note that similar weight 4 stabilizers have recently been implemented in superconducting qubits ( 23). In addition to the error checks provided by stabilizer measurements, only even-parity outcomes are accepted when the data qubits are measured at the end of the circuit. Both stabilizer measurements serve to determine the overall yield, that is, the fraction of runs for which no error was indicated. Because we prepare eigenstates of logical Pauli operators, only logical Pauli operations that change the ideal state result in errors. With only one ancilla qubit available, we measure the two stabilizers in separate experiments. Measuring the ancilla yields either |0〉, indicating no error, or |1〉, meaning an error has occurred and the run is to be discarded.

Applying these stabilizers conditional on the state of an ancilla qubit extracts the parity of the data qubits along X or Z (see Fig.

The difference is that the stabilizers have weight 4 because we simultaneously extract information about the gauge qubit L b.

#Thresholds of quantum error correction codes code

As in a Bacon-Shor code block ( 20, 21), the code space together with the logical operators and stabilizers form a subsystem that allows local syndrome extraction similar to that of Napp and Preskill ( 22), as depicted in Fig.