{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"802f386631922b6fec17012bffce91d34cd84be571468c8f7fb06005fa144086","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["a54a341fc4bc03990e8c80a2d8e5a4890eeeeed62b2e46ebc85fc011e1166b14","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"e4677d0f3922f75805d7e5f1eed86023e899028dd8e45958a77601fa21ea8d9f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":["ai:gpt-5.5"],"external_id":"qi.qldpc-codes.constant-overhead-ft","kind":"well-posed","literature_status":"open","n":"2","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 $O \\sim (\\mathrm{log} N)$ 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":"a54a341fc4bc03990e8c80a2d8e5a4890eeeeed62b2e46ebc85fc011e1166b14","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ce88f23d75b7b43c402ee0211c083bc124b4ae5cb8faecc743f6c13edb2ce9cb","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"97495335f53de07b5afbed9ce0800dd11217a7f4058c5f37feb8fd6a0e19fd3a","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"_dBIg1KxYTtmfX0I3_9dhlEDCtc0NNFxvB0Z1ZMJImoNLcFQCS9JhsFN5K0vIPYSCLOd4IUMmfRwTAVDLeNgAQ"},"schema":"pubphys.envelope/1"},"record_hash":"ce88f23d75b7b43c402ee0211c083bc124b4ae5cb8faecc743f6c13edb2ce9cb","leaf_index":3736}