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In this paper, we present a resource-efficient 4-qubit quantum circuit designed to detect and correct single-qubit bit-flip errors within a 3-qubit data block. The circuit uses Feynman (CNOT) and NOT gates alongside an ancillary qubit to implement full correction logic with minimal overhead. Compared to well-known approaches like the 9-qubit Shor code, our design achieves equivalent fidelity (100%) using fewer qubits, making it highly suitable for near-term quantum devices. Simulation results, obtained using IBM Quantum Composer and Qiskit, confirm the circuit\u2019s correctness and reliability across all bit-flip scenarios. The design also introduces a reusable unitary block for efficient implementation. This work offers a scalable and practical solution to quantum error correction using minimal hardware resources.<\/jats:p>","DOI":"10.2478\/qic-2025-0019","type":"journal-article","created":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T13:59:48Z","timestamp":1755871188000},"page":"344-355","source":"Crossref","is-referenced-by-count":0,"title":["A Resource-Efficient 4-Qubit Circuit for Bit-Flip Error Correction Using Feynman Gates"],"prefix":"10.2478","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9379-1319","authenticated-orcid":false,"given":"Dimitrios","family":"Gryllakis","sequence":"first","affiliation":[{"name":"Electrical and Computer Engineering Department, University of Patras , Patras , Greece"},{"name":"AI-Hub, University of Patras , Patras , Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1797-1343","authenticated-orcid":false,"given":"Kyriakos N.","family":"Sgarbas","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering Department, University of Patras , Patras , Greece"},{"name":"AI-Hub, University of Patras , Patras , Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2025,8,22]]},"reference":[{"key":"2026052407150635254_j_qic-2025-0019_ref_001","doi-asserted-by":"crossref","unstructured":"P.W. Shor (1995). \u201cScheme for reducing decoherence in quantum computer memory.\u201d Physical Review A, 52, R2493(R). https:\/\/journals.aps.org\/pra\/abstract\/10.1103\/PhysRevA.52.R2493","DOI":"10.1103\/PhysRevA.52.R2493"},{"key":"2026052407150635254_j_qic-2025-0019_ref_002","doi-asserted-by":"crossref","unstructured":"A.G. Fowler, M. Mariantoni, J.M. Martinis and A.N. Cleland (2012). \u201cSurface codes: Towards practical large-scale quantum computation.\u201d Physical Review A, 86, 032324. https:\/\/doi.org\/10.1103\/PhysRevA.86.032324","DOI":"10.1103\/PhysRevA.86.032324"},{"key":"2026052407150635254_j_qic-2025-0019_ref_003","unstructured":"M.R.A. Newman, \u201cRepetition Code.\u201d Prefetch, https:\/\/prefetch.eu\/know\/concept\/repetition-code\/"},{"key":"2026052407150635254_j_qic-2025-0019_ref_004","unstructured":"S. Krinner et al. (2021). \u201cRealizing repeated quantum error correction in a distance-three surface code.\u201d https:\/\/arxiv.org\/abs\/2112.03708"},{"key":"2026052407150635254_j_qic-2025-0019_ref_005","unstructured":"D. Gottesman (2009). \u201cAn introduction to quantum error correction and fault-tolerant quantum computation.\u201d https:\/\/arxiv.org\/abs\/0904.2557"},{"key":"2026052407150635254_j_qic-2025-0019_ref_006","unstructured":"A.M. Steane (2006). \u201cA tutorial on quantum error correction.\u201d in International School of Physics \u201cEnrico Fermi.\u201d IOS Press. https:\/\/www2.physics.ox.ac.uk\/sites\/default\/files\/ErrorCorrectionSteane06.pdf"},{"key":"2026052407150635254_j_qic-2025-0019_ref_007","unstructured":"J. Preskill (1999). \u201cQuantum error correction.\u201d Quantum Computation Lecture Notes, Chapter 7, http:\/\/theory.caltech.edu\/~preskill\/ph219\/index.html"},{"key":"2026052407150635254_j_qic-2025-0019_ref_008","unstructured":"J. Watrous (2006). \u201cQuantum error correction (Lecture 16).\u201d CPSC 519\/619, University of Calgary. https:\/\/cs.uwaterloo.ca\/~watrous\/QC-notes\/QC-notes.16.pdf"},{"key":"2026052407150635254_j_qic-2025-0019_ref_009","doi-asserted-by":"crossref","unstructured":"S.M. Girvin (2023). \u201cIntroduction to quantum error correction and fault tolerance.\u201d SciPost Physics Lecture Notes, 70, https:\/\/scipost.org\/SciPostPhysLectNotes.70\/pdf","DOI":"10.21468\/SciPostPhysLectNotes.70"},{"key":"2026052407150635254_j_qic-2025-0019_ref_010","doi-asserted-by":"crossref","unstructured":"R. Padma Priya, A. Baradeswaran (2018). \u201cAn efficient simulation of quantum error correction codes.\u201d Alexandria Engineering Journal, 57, 3, https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1110016817302089","DOI":"10.1016\/j.aej.2017.06.013"},{"key":"2026052407150635254_j_qic-2025-0019_ref_011","unstructured":"A. Chatterjee, K. Phalak, S. Ghosh, \u201cQuantum error correction for dummies.\u201d arXiv:2304.08678v2 [quant-ph], https:\/\/arxiv.org\/abs\/2304.08678"},{"key":"2026052407150635254_j_qic-2025-0019_ref_012","unstructured":"J.R. Wootton and D. Loss, \u201cA repetition code of 15 qubits.\u201d arXiv:1709.00990v3 [quant-ph], https:\/\/arxiv.org\/abs\/1709.00990"},{"key":"2026052407150635254_j_qic-2025-0019_ref_013","unstructured":"M. Kastoryano, \u201cQuantum error correction.\u201d Lecture Notes, University of Cologne, 2018\u20132019, https:\/\/www.thp.uni-koeln.de\/kastoryano\/ExSheets\/Notes_v6.pdf"},{"key":"2026052407150635254_j_qic-2025-0019_ref_014","doi-asserted-by":"crossref","unstructured":"M. Vahabi, E. Rahimi, P. Lyakhov, A.N. Bahar, K. Wahid, A. 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