t b a b a

the original codeword. Now we need to apply the syndrome measurement on the
original codeword. If no corresponding actions applied on the ancilla, this syndrome
measurement will destroy the codeword because of the entanglement. Therefore, to
protect the codeword, the extended syndrome measurement need apply corresponding
actions on the ancilla, which preserves the entanglement between the codeword and
the ancilla.
3. Stabilizer: The extended syndrome measurement is built of new stabilizers: these new
stabilizers (or generators) should also stabilize the codeword and satisfy all the stabiliz-
ers’ requirements. Therefore, the new stabilizers should commute with all codewords,
and commute with each other. Also at least one of them anti-commutes with the error
we want to correct.
4. Disentanglement: After the extended syndrome measurement, we should be able to
restore the original codeword - disentangle the ancilla from the codeword. This process
should restore the original codeword to its initial status.
5. Distinct syndrome: Since the new code need to correct one more error than the original
code, it must have distinct syndromes for different error combinations. Thus, these
error combinations can be identified and corrected.
6. Error propagation: The algorithm uses some ancilla to duplicate the qubit with error
in the last error correction cycle. However, these ancilla may also be influenced by
90