{"schema":"research-release/1","title":"Nineteen qubits are necessary and sufficient for symmetric quantum codes correcting two errors","author":"Yuxuan Zhang","affiliation":null,"version":"1.0","date":"2026-11-10","original_url":"https://qiqc-op.com/problem/op_a72722e455d85d55/","website_url":"https://yuxuanzhang1995.github.io/agentic-research/symmetric-two-error-code-length/","status":"complete proof candidate; independent model review","original_coverage":"complete","review":{"fresh_context":true,"same_model_family":true,"separate_derivations_and_controls":true,"external_expert":false,"formal_proof_assistant":false,"report_in_zip":"review/REVIEW.md","sources_in_zip":"review/SOURCES.md","assessment_sha256":"d0c8aee7476d82e2e5044762bdc49b8d0a1d5d87a7c25af26398f26f2f4d6b50"},"contribution":"Exact exclusion at eighteen qubits; matching nineteen-qubit upper bound is published prior work. Earlier scalar bounds below eighteen are credited.","files":{"symmetric-two-error-code-length-v1.pdf":"45746acd997d99bc7758b3c739319e8d95a41d84dd67b8af84f93d821e780aad","symmetric-two-error-code-length-v1.zip":"b1acb77d481df6cbed4d04b8d1c2caddee2d2f02997dbc2eae62930c134c1f9f"},"source_sha256":"d689dcffe7de1e2412c818a849bd5828c80c97a37594eb244503bc72138c01d6","candidate_sha256":"b107acbbd50bf51aec366524902676686a9eff34b93c42c79690963f1a5b6373","package_manifest_sha256":"9aeca74049efaf943912766c437ded1431420a3cde3eaf4ab883867941777d63","certificate_lengths":[9,10,11,12,13,14,15,16,17,18],"scalar_multipliers":435,"positive_rational_matrix_pivots":2496,"limitations":["No external expert review","No proof-assistant formalization","No independent rerun of AAB nineteen-qubit polynomial root isolation","Bounded literature search is not exhaustive universal priority certification"],"external_status":{"journal_review":false,"arxiv_submission":false,"catalogue_acceptance":false}}