{"paper":{"title":"Foliated Quantum Error Correction for Qudits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"G\\\"ozde \\\"Ust\\\"un, Jason Saied, Simon J. Devitt","submitted_at":"2026-07-15T12:40:56Z","abstract_excerpt":"We present a framework for foliating any Pauli-based quantum error-correcting code over prime-dimensional qudits. For any such code, we obtain a qudit graph state that can be measured to perform fault-tolerant measurement-based quantum computing. Such a paradigm is of interest in platforms such as photonics, where measurement-based protocols are natural and high-dimensional states are readily available. We discuss several examples for arbitrary prime dimension $d$, such as the qudit toric code (stabilizer, CSS), the $d$-dimensional perfect $[[5,1,3]]$ code (stabilizer, non-CSS), and a straight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13784","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13784/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}