{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"6702ff66773819e8d721742f491ab737dd7351409238ff01cdacc240b29de6d2","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"63543faf1c7b11e605cac13399a0a2944998ad277d52d892dfdb609e9a70a146","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"qi.qldpc-codes.logical-gates-qldpc","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Storing quantum information in these codes is understood far better than computing with it. A way to apply every needed operation to the stored qubits without giving back the qubit savings is still missing in practice.","posed_since":"","precise":"For a constant-rate qLDPC family with distance d, give a fault-tolerant implementation of a universal logical gate set (all logical Clifford gates plus one non-Clifford gate on any chosen logical qubits) that uses O(n) ancilla qubits, has space-time cost per logical gate O(d polylog d), and has a threshold under circuit-level noise. Candidate ingredients include code surgery, code automorphisms and codes with transversal CCZ.","problem_ref":null,"references":"","settled_by":"An explicit gate scheme with stated overhead and a threshold proof or convincing circuit-level simulation at relevant sizes.","status_note":"Several 2024-2026 schemes cover parts of the gate set at moderate overhead.","title":"Low-overhead universal logical gates on constant-rate qLDPC codes","topic_ref":"71196b612de8cb112565b0581c5d9a20e4fcd90e9f372725435ebd01a1125190"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"03bf09b3265758b7ecee8d02fabceb567cf88e747132293afbd8dce7d0f68646","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"591759cc5ca46ee2db69bb3b947e825d0019d6367c517c830c81c8158cf872bb","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"lLDNDR6EKwzUjMPY3bh-YDBFDXwdgbMX2C5Dg7kZf_9Y_Z-_pCdqa2inSboJY2yCFcmkLqlfCA6GMOg2Y8dzDA"},"schema":"pubphys.envelope/1"},"record_hash":"03bf09b3265758b7ecee8d02fabceb567cf88e747132293afbd8dce7d0f68646","leaf_index":2025}