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Despite significant advancements in quantum hardware, scalability remains a challenge, with errors accumulating as more qubits and gates are added. To overcome this limitation, quantum error-correction codes have been introduced. Although the success of quantum error correction codes has been demonstrated on superconducting quantum processors \\cite{ibm_rep,ibm_bell,google_qec1,google_qec2} and neutral atom-based systems \\cite{neutral}, there have been no experimental reports of error suppression using flag qubits on a quantum processor. IBM\u2019s quantum hardware features a non-topological coupling map, and past developments of quantum error correction codes on this platform have primarily explored the use of 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 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.<\/jats:p>","DOI":"10.22331\/q-2025-10-23-1893","type":"journal-article","created":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T12:08:14Z","timestamp":1761221294000},"page":"1893","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Effectiveness of the syndrome extraction circuit with flag qubits on IBM quantum hardware"],"prefix":"10.22331","volume":"9","author":[{"given":"Younghun","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Applied Physics, Hanyang University(ERICA), Ansan 15588, Republic of Korea"}]},{"given":"Hansol","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Hanyang University(ERICA), Ansan 15588, Republic of Korea"}]},{"given":"Jeongsoo","family":"Kang","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Hanyang University(ERICA), Ansan 15588, Republic of Korea"}]},{"given":"Wonjae","family":"Choi","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Hanyang University(ERICA), Ansan 15588, Republic of Korea"}]},{"given":"Younghun","family":"Kwon","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Hanyang University(ERICA), Ansan 15588, Republic of Korea"}]}],"member":"9598","published-online":{"date-parts":[[2025,10,23]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. R. Wootton and D. Loss. ``Repetition code of 15 qubits''. Physical Review A 97, 052313 (2018).","DOI":"10.1103\/PhysRevA.97.052313"},{"key":"1","doi-asserted-by":"publisher","unstructured":"B Het\u00e9nyi and J. R. Wootton. ``Creating entangled logical qubits in the heavy-hex lattice with topological codes''. PRX Quantum 5, 040334 (2024).","DOI":"10.1103\/PRXQuantum.5.040334"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Google Quantum AI. ``Exponential suppression of bit or phase errors with cyclic error correction''. Nature 595, 383 (2021).","DOI":"10.1038\/s41586-021-03588-y"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Google Quantum AI. ``Suppressing quantum errors by scaling a surface code logical qubit''. Nature 614, 676\u2013681 (2023).","DOI":"10.1038\/s41586-022-05434-1"},{"key":"4","doi-asserted-by":"publisher","unstructured":"D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. 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Kitaev. ``Fault-tolerant quantum computation by anyons''. Ann. Phys. 303, 2\u201330 (2003).","DOI":"10.1016\/S0003-4916(02)00018-0"},{"key":"10","doi-asserted-by":"publisher","unstructured":"A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland. ``Surface codes: towards practical large-scale quantum computation''. Phys. Rev. A 86, 032324 (2012).","DOI":"10.1103\/PhysRevA.86.032324"},{"key":"11","doi-asserted-by":"publisher","unstructured":"B. M. Terhal. ``Quantum error correction for quantum memories''. Rev. Mod. Phys. 87, 307 (2015).","DOI":"10.1103\/RevModPhys.87.307"},{"key":"12","doi-asserted-by":"publisher","unstructured":"S. Bravyi and A. Kitaev. ``Universal quantum computation with ideal clifford gates and noisy ancillas''. Phys. Rev. A 71, 022316 (2005).","DOI":"10.1103\/PhysRevA.71.022316"},{"key":"13","doi-asserted-by":"publisher","unstructured":"C. Chamberland, P. Iyer, and D. 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