Generalizing Pauli Checks for Qudit-based Quantum Error Detection and Mitigation

Quantum Physics arXiv:2608.18332 (quant-ph) [Submitted on 18 Aug 2026] Title:Generalizing Pauli Checks for Qudit-based Quantum Error Detection and Mitigation Authors:Noble Agyeman-Bobie, Quinn Langfitt, Salahedeen Issa, Nikos Hardavellas, Kaitlin N. Smith View a PDF of the paper titled Generalizing Pauli Checks for Qudit-based Quantum Error Detection and Mitigation, by Noble Agyeman-Bobie and 4 other authors View PDF HTML (experimental) Abstract:Pauli Check Sandwiching (PCS) is a quantum error detection (QED) technique that protects a quantum circuit by utilizing a pair of controlled Pauli operators, or checks, and detecting errors that anti-commute with the checks. Further, PCS can be used for quantum error mitigation (QEM) via post-selection based on the Pauli check syndrome values. Currently, PCS is leveraged in the qubit space. In this paper, we introduce a generalized approach for applying PCS-based QED and QEM to quantum information of arbitrary dimension in the Hilbert space. Each pair of these extended checks consists of a sequence of gates in the Heisenberg-Weyl operator set that extend Pauli operators into the qudit space. These qudit checks use at least one ancilla qudit to detect qudit errors that do not commute with the unitary selected for the check. We show that our proposed methods for qudit QED can detect errors of arbitrary dimensions. More specifically, we prove that an arbitrary Heisenberg-Weyl error maps deterministically to a unique ancilla readout, and further, post-selecting on the $|0 \rangle$ readout guarantees unit fidelity in the noiseless check limit. We validate these findings numerically across dimensions $d=2$ through $d=9$, achieving error-mitigated fidelities above $97.5\% $ under realistic depolarizing error rates. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.18332 [quant-ph] (or arXiv:2608.18332v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.18332 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Quinn Langfitt [view email] [v1] Tue, 18 Aug 2026 21:31:59 UTC (637 KB) Full-text links: Access Paper: View a PDF of the paper titled Generalizing Pauli Checks for Qudit-based Quantum Error Detection and Mitigation, by Noble Agyeman-Bobie and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?) 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?)