  Large-scale quantum circuits are required to exploit the advantages of
quantum computers. Present-day quantum computers have become less reliable with
increasing depths of quantum circuits. To overcome this limitation, quantum
error-correction codes have been introduced. Although the success of quantum
error correction codes has been announced in Google[1, 2] and neutral atom[3]
quantum computers, there have been no reports on IBM quantum computers showing
error suppression owing to its unique heavy-hexagon structure. This structure
restricts connectivity, and quantum error-correction codes on IBM quantum
computers require flag qubits. Here, we report the successful implementation of
a syndrome extraction circuit with flag qubits on IBM quantum computers.
Moreover, we demonstrate its effectiveness by considering the repetition code
as a test code among the quantum error-correcting codes. Even though the data
qubit is not adjacent to the syndrome qubit, logical error rates diminish
exponentially as the distance of the repetition code increases from three to
nine. Even when two flag qubits exist between the data and syndrome qubits, the
logical error rates decrease as the distance increases similarly. This confirms
the successful implementation of the syndrome extraction circuit with flag
qubits on the IBM quantum computer.
