{"paper":{"title":"Quantum Precoded Polar Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Rate-1 precoded polar codes yield CSS quantum codes with logical error rates matching a much larger surface code.","cross_cats":["math.IT","quant-ph"],"primary_cat":"cs.IT","authors_text":"Matthieu R. Bloch, Shrinivas Kudekar, Tyler Kann","submitted_at":"2026-05-12T22:25:00Z","abstract_excerpt":"We introduce a new family of CSS codes obtained from rate-1 precoded polar codes, which harnesses the precoding benefits obtained for classical short blocklength polar codes. We optimize the rate profile and precoder of these codes with a genetic algorithm, and present codes of dimension $ [\\![256, 2 ]\\!] $ and $ [\\![512, 2]\\!] $ that have logical error rates similar to the $ [\\![1201, 1, 25 ]\\!] $ surface code over the depolarizing channel."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We present codes of dimension [[256, 2]] and [[512, 2]] that have logical error rates similar to the [[1201, 1, 25]] surface code over the depolarizing channel.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The benefits of classical rate-1 precoding for short-blocklength polar codes transfer directly to the quantum CSS setting after genetic-algorithm optimization of the rate profile and precoder.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quantum CSS codes derived from precoded polar codes match the logical error performance of a large surface code at small block lengths [[256,2]] and [[512,2]] over depolarizing noise.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Rate-1 precoded polar codes yield CSS quantum codes with logical error rates matching a much larger surface code.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fb8c78c2f11f81d74373fc0e7790122254f6a8100d1503613abdbcbe5b7179b2"},"source":{"id":"2605.12796","kind":"arxiv","version":1},"verdict":{"id":"d130ae68-982c-45c2-aedf-90cef59f776d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:22:58.051999Z","strongest_claim":"We present codes of dimension [[256, 2]] and [[512, 2]] that have logical error rates similar to the [[1201, 1, 25]] surface code over the depolarizing channel.","one_line_summary":"Quantum CSS codes derived from precoded polar codes match the logical error performance of a large surface code at small block lengths [[256,2]] and [[512,2]] over depolarizing noise.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The benefits of classical rate-1 precoding for short-blocklength polar codes transfer directly to the quantum CSS setting after genetic-algorithm optimization of the rate profile and precoder.","pith_extraction_headline":"Rate-1 precoded polar codes yield CSS quantum codes with logical error rates matching a much larger surface code."},"references":{"count":26,"sample":[{"doi":"","year":1997,"title":"Gottesman,Stabilizer codes and quantum error correction","work_id":"c43c2cf6-082c-4a22-ae91-b8ab7242b8ff","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1996,"title":"Good Quantum Error-Correcting Codes Exist,","work_id":"13375479-1efe-4258-9ec4-86442696d445","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1954,"title":"Multiple-particle interference and quantum error correction,","work_id":"6bd491d0-a541-46e2-87c7-e294fc8da2a2","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"Efficient Polar Coding of Quantum Information,","work_id":"7e3eaf2c-a973-495d-a2d8-69552e8ac6ef","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Fault-tolerant preparation of quantum polar codes encoding one logical qubit,","work_id":"bd6ad896-5ebe-4ef0-8c1b-7855e9d6b513","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":26,"snapshot_sha256":"3fd95a94693b54a78726692419db5a0793ecd67103ee8163109fd06d783645bf","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"}