{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"468391a89e5047d5186ec34cfccff9791e682dcdb213036090a97040ce7af4a6","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d7714267efc0d2e12463476adf2b793b1c95952b6d4c4a20d7d2f66387cd15cd","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.qldpc-codes.constant-overhead-ft","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Theorists can now run a quantum computation reliably with only a constant factor more qubits, but at the price of a slowdown that grows slowly with problem size. Whether both the qubit cost and the slowdown can be constant at once is unknown.","posed_since":"2013","precise":"For quantum circuits on $N$ logical qubits of depth $\\operatorname{poly}(N)$ under local stochastic noise below a constant threshold, does a fault-tolerance scheme exist with physical-to-logical qubit ratio $O(1)$ and time overhead $O(1)$? Gottesman (2013) gave constant space with polynomial time overhead; schemes from 2024 reach constant space with polylogarithmic or O~(log N) time overhead (arXiv:2411.03632, arXiv:2411.03683). An answer is a construction or a lower bound proving that $\\omega(1)$ time overhead is necessary at constant space overhead.","problem_ref":null,"references":"","settled_by":"An explicit constant-space, constant-time fault-tolerance scheme with a threshold proof, or a matching lower bound on time overhead.","status_note":"2024 constructions reduced the time overhead to about log N at constant space overhead.","title":"Fault tolerance with constant space and constant time overhead","topic_ref":"71196b612de8cb112565b0581c5d9a20e4fcd90e9f372725435ebd01a1125190"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"a54a341fc4bc03990e8c80a2d8e5a4890eeeeed62b2e46ebc85fc011e1166b14","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"95eae12e1e67fbca3199195b1b85b51c823edcfdc6976362830692504a7ed8a7","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"CPSfwk_1UYZ2KBFIMneor5IXBV_qJG0oM7jpXKvSDvpFa0Cu2IFcoduM6Tqk_DGZhvKLJylNyAV-CVgELj8TAg"},"schema":"pubphys.envelope/1"},"record_hash":"a54a341fc4bc03990e8c80a2d8e5a4890eeeeed62b2e46ebc85fc011e1166b14","leaf_index":2024}