Fault-Tolerant Quantum Error Correction: Implementing Hamming-Based Codes with Advanced Syndrome Extraction Techniques
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Quantum Physics arXiv:2601.07860 (quant-ph) [Submitted on 10 Jan 2026] Title:Fault-Tolerant Quantum Error Correction: Implementing Hamming-Based Codes with Advanced Syndrome Extraction Techniques Authors:Soham Bhadra, Diyansha Singh, Angana Chowdhury View a PDF of the paper titled Fault-Tolerant Quantum Error Correction: Implementing Hamming-Based Codes with Advanced Syndrome Extraction Techniques, by Soham Bhadra and 2 other authors View PDF HTML (experimental) Abstract:Building reliable quantum computers requires protecting fragile quantum states from inevitable environmental noise and operational errors. While quantum error correction codes like the Steane $[\![7,1,3]\!]$ code provide elegant theoretical solutions, their practical success hinges critically on how we measure errors - a process called syndrome extraction. The challenge lies in the ancilla qubits used for measurement: when they fail, errors can cascade across the entire quantum system, destroying the very information we're trying to protect. We address this fundamental problem by implementing and comparing three sophisticated syndrome measurement strategies: Shor's cat-state approach, which distributes measurements across multiple entangled ancillas achieving 85-92% preparation success; Steane's encoded-ancilla method using complete error-corrected logical qubits reaching 97.8% syndrome fidelity; and a flexible unified framework that adapts strategies based on hardware capabilities. Through extensive simulations using IBM's Qiskit platform spanning randomized benchmarking and T-heavy circuits, we demonstrate that intelligent ancilla management improves error suppression by up to 2.4$\times$ compared to standard approaches. Our implementations achieve logical error rates as low as $5.1 \times 10^{-5}$ under realistic noise conditions with physical error rates of $10^{-3}$, while maintaining near-unity logical fidelity (0.99997) even for deep circuits. The threshold analysis reveals robust performance across distance-3 to distance-13 codes with characteristic threshold curves showing exponential error suppression below the critical physical error rate. These results provide immediately deployable tools for near-term quantum devices and establish practical design principles for scaling toward fault-tolerant quantum computers. Subjects: Quantum Physics (quant-ph); Emerging Technologies (cs.ET) Cite as: arXiv:2601.07860 [quant-ph] (or arXiv:2601.07860v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.07860 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Diyansha Singh [view email] [v1] Sat, 10 Jan 2026 00:10:52 UTC (449 KB) Full-text links: Access Paper: View a PDF of the paper titled Fault-Tolerant Quantum Error Correction: Implementing Hamming-Based Codes with Advanced Syndrome Extraction Techniques, by Soham Bhadra and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cs cs.ET References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)