{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3c23a882455b70f4cad09e88c8e7be722e70642dbe8c1952d14ff06b5e013886","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"881e9ba4714badbd4af353fde338e5f950d5248b777eb9a4a3566639fa578691","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.hamiltonian-complexity.good-quantum-ltc","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"A locally testable code lets a checker detect a corrupted message by looking at a few randomly chosen checks, with failure probability growing with the amount of corruption. Quantum versions with good size and error tolerance would be a step toward the quantum PCP conjecture, and their existence is open.","posed_since":"","precise":"Does a family of quantum stabilizer codes exist with $O(1)$-weight checks, rate $k/n = \\Omega(1)$, relative distance $d/n = \\Omega(1)$, and constant soundness: the fraction of violated checks is at least c times the relative distance of the state from the code space? Dinur, Lin and Vidick (arXiv:2402.07476) give constant rate with inverse-polylogarithmic distance and soundness.","problem_ref":null,"references":"","settled_by":"An explicit good qLTC family with proofs of all three parameters, or a no-go theorem.","status_note":"Almost-good qLTCs (constant rate, inverse-polylog distance and soundness) were constructed in 2024, with the rate analysis corrected in a 2025 revision.","title":"Existence of good quantum locally testable 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