{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"908508376754d54d79c7884a3c61664f2d1fb748ff0606109972c06e1a2568f9","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["217257a5473e2dddd9b73f7b21e46325849fe0a9c53b581d56985d4e508ae2d6","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"b4279a851dec47621822ad5cc7db0b9d3264498c6aebde819155f993ae4ed01c","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.fault-tolerance-noise.long-range-correlated-threshold","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Error correction is proven to work when errors on distant qubits are nearly independent. It is unknown whether it still works when each qubit feels a fixed amount of noise but a shared environment links the noise on far-apart qubits with correlations that fall off slowly with distance.","posed_since":"2006","precise":"Qubits on a $D$-dimensional lattice couple through $H_{\\int} = \\sum_i \\sigma_i B_i$ to a Gaussian bath with fixed single-qubit noise strength $\\langle B_i B_i\\rangle$ and spatial correlations $\\langle B_i(t) B_j(t')\\rangle$ decaying as $\\left|r_i - r_j\\right|^{-\\alpha}$. A threshold is proved when the system-bath coupling decays faster than $1/r^D$ (Aharonov, Kitaev and Preskill, Phys. Rev. Lett. 96, 050504, 2006, arXiv:quant-ph/0510231). Decide whether a positive threshold in the single-qubit noise strength exists for $\\alpha \\le D$, or prove a logical-error floor independent of code size.","problem_ref":"217257a5473e2dddd9b73f7b21e46325849fe0a9c53b581d56985d4e508ae2d6","references":"","settled_by":"A threshold proof for the stated Gaussian-bath model with $\\alpha \\le D$, or a proof of a size-independent logical-error floor for it.","status_note":"Rigorous threshold proofs (2006, 2009, 2013) assume summable correlations; the slowly decaying case has only non-rigorous treatments.","title":"Threshold theorem for noise with slowly decaying spatial correlations","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"fa48aab678fe88b9978548e23b949c2a9437f0b8f319f9afc0e978c64c226e5d","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"41da1537ca6c46b063faa8260ea9c947d56510bc9a7a6ce801d1c5b20aeb0c7b","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"yPfR32WrAhqVeYepQrAcfXMfQfD8TrhjF87W4BEvDQTIE3ULQsEGFYh2Y-VQ4jvsg50CyV9EQixwaDcbIf_ZAg"},"schema":"pubphys.envelope/1"},"record_hash":"fa48aab678fe88b9978548e23b949c2a9437f0b8f319f9afc0e978c64c226e5d","leaf_index":3710}