Figure 4: Error detection.
From: Experimental demonstration of a graph state quantum error-correction code
(a) Z errors on one of the qubits of the code flips the sign of the expectation value of one or two of the stabilizer (syndrome) operators S1, S2 and S3, as can be seen in the tables showing the experimental values for the four probe states. The values range from 0.66 to 0.79 in magnitude. The syndrome operators correspond to joint measurements, thus they can in principle be measured without disturbing the state. If no error has occurred the code can continue to be used. If an error has occurred then it will be detected and the ancilla can be encoded again to allow the continuation of a given protocol. If the error is known to be a Z Pauli operation then its location can be detected and corrected. If it is not, the ancilla must be re-encoded to allow the continuation of a given protocol. (b) Y errors on one of the qubits of the code also flips the sign of the expectation value of one or two of the syndrome operators. If the error is known to be a Y Pauli operation then its location can be detected and corrected. If not, the ancilla can again be re-encoded. (c) X errors on one of the qubits of the code flips the sign of the expectation value of all the syndrome operators. Note that if the location of the error is known, then the type of error can be inferred from the pattern of the expectation values of the syndrome operators and the error can be corrected.
