{"paper":{"title":"Magic State Distillation via Codes over Binary Extension Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Adam Wills, Anqi Gong, Christopher A. Pattison, Patrick Rall","submitted_at":"2026-08-10T15:26:12Z","abstract_excerpt":"Fault-tolerant quantum computation architectures are frequently bottlenecked by the overhead of producing high-fidelity magic states. In this work, we use algebraic geometric techniques to construct codes over binary extension fields $\\mathbb{F}_{2^s}$, thus discovering new protocols for the distillation of qubit magic states, where our focus is on the regime of practical qubit-based quantum computing architectures. To do this, we show that multi-qubit gates of interest such as $\\text{CS}$, $\\text{CCZ}$, and $\\text{TOF}\\# = \\text{CCZ}_{123}\\text{CCZ}_{345}$, can be packaged into simple gates o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09727","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/2608.09727/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"}