Fault-tolerant logical qubits can be demonstrated with logical error rates that improve as error-correcting code distance increases.
Evidence is materially increasing confidence in—or pressure on—the claim; significant uncertainty remains. State definitions
No evidence has been admitted since this assessment.
Retained questions may have been narrowed or reframed by the current assessment.
Verification position derived from the record’s assessments; dates show when Faultline first recorded each stage.
LPR identifies an internal source-review record. PROG identifies a programme: AI (Artificial Intelligence), AM (Advanced Materials), BT (Biotechnology), or QE (Quantum Engineering).
How the claim could hold, what obstructs it, and possible ways forward. The State Warrant above remains the authoritative current assessment.
Physical qubit error floor. Surface code performance depends on physical qubit error rates remaining below the fault-tolerance threshold (approximately 1% for surface codes). Current superconducting qubit systems operate near this threshold; trapped-ion systems are below it. Any degradation in physical qubit performance with increased system size — due to crosstalk, control errors, or fabrication variability — could prevent the scaling behaviour from holding at larger code distances. This mechanism has not produced contesting evidence in the current evidence trail but is the primary physical constraint on extrapolation.
Demonstrated distance versus required distance. The claim's empirical signature has been demonstrated at code distances d=3 to d=7. Practical fault-tolerant computation for useful algorithms requires code distances in the range d=20 to d=50, implying physical qubit counts of thousands to tens of thousands per logical qubit. The scaling behaviour observed at small distance must hold at large distance for the claim to have full practical force. The claim as stated does not require large-distance demonstration — it requires demonstration of the behaviour — and that has been achieved. The bottleneck is between the claim as stated and its practical consequence, not within the claim itself.
A recorded possible resolution path, not automatically a sufficient test for closing the claim.
Below-threshold operation as resolution point. The below-threshold result in INST-005 (Google Willow) represents a qualitative threshold that, if confirmed at increasing code distances, would provide material evidence for a governed assessment of whether the claim has reached resolution. Below-threshold operation means the scaling behaviour is not merely demonstrated but is self-reinforcing: each additional qubit added to the code actively improves logical error rates. If this holds at d=11 and d=15, the claim trajectory moves toward RESOLVING. The attractor is the below-threshold confirmation at larger distances, which is the next expected evidence event in this record.
Historical narrative recorded for this claim. It does not override the current State Warrant.
Questions retained in this record. The current State Warrant may have narrowed or reframed them. Recorded dates refer to question history, not necessarily the age of the current wording; known revision dates are shown separately.
Does below-threshold scaling behaviour hold at code distances d=11 and above? This is the next decisive measurement. If it does, the claim approaches RESOLVING. If it does not, the claim requires reassessment of whether small-distance results generalise.
Question recorded 2024-01-15The claim is architecture-agnostic, but all current strong evidence comes from superconducting (Google) and trapped-ion (Quantinuum) systems. Microsoft's topological qubit programme is currently tracked as contextual evidence within the Quantum Engineering corpus rather than through a dedicated Frontier Record. How should future evidence relating to this programme be represented within the Observatory?
Question recorded 2024-01-15The claim as stated is close to resolution. If RESOLVING is the next pressure state, what would constitute sufficient evidence to issue a RESOLVING assessment? The claim needs a resolution criterion that is as precise as the claim itself. No governed procedure currently specifies this.
Question recorded 2024-01-15| Mutation | Date | Field | Prior value | Current value |
|---|---|---|---|---|
| M-016 | 2026-10-24 | Editorial correctioneditorial_correction | ATTRACTOR wording assigned a governed institutional consequence directly to the future evidence event | ATTRACTOR wording preserves the evidence route while reserving State, Stage, verdict or reopening consequences to governed assessmentWhat this update recorded for M-016Operator-authorised A4 institutional-authority consistency repair. Correct AT-001 explanatory wording only; no new evidence, scientific threshold, evidence target, Pressure State, Verification Stage, assessment or ATTRACTOR identity changed. This repair is independent of the closed ATTRACTOR taxonomy v2 FAIL. Receipt: docs/reviews/A4-INSTITUTIONAL-AUTHORITY-CONSISTENCY-REPAIR-2026-10-24.json. |
| M-015 | 2026-10-19 | Reference correctionreference_corrected | Shared citations not explained in the evidence list | Source-specific reciprocal notices on IN-006What this update recorded for M-015Operator-authorised corpus reading audit Step 5A / R04. Label exact shared publications/reports after checking their evidential roles. Shared reporting does not by itself determine experimental independence. No sources, scientific wording, vectors, counts, assessments, states, stages, dates, review markers or prior mutations changed. Scope, primary-source ledger and exact field receipt: docs/reviews/SHARED-SOURCE-LABELS-STEP-5A-2026-10-19.md and companion .json. |
| M-014 | 2026-10-19 | Reference correctionreference_corrected | Existing source-review limitation not fully exposed in evidence-list status | Explicit reviewed evidence status on IN-001, IN-002, IN-003, IN-004What this update recorded for M-014Operator-authorised corpus reading audit Batch 3 / R02. Render the existing entry-level review disposition from explicit status metadata linked to its retained review and mutation. A withdrawn attribution is not a retracted publication; missing sources and Partial polarity do not automatically determine status. Preserve all original titles, descriptions, citations, counts, assessments, review markers and prior mutations. No substitute source, new evidence or reassessment. Receipt: docs/reviews/EVIDENCE-STATUS-BATCH-3-2026-10-19.md. |
| M-013 | 2026-09-13 | Source reviewprovenance_review | — | LPR-001-D15What this update recorded for M-013Legacy provenance review completed. All six evidence instances examined. IN-005 and IN-006 were cleanly provenance-enriched with the peer-reviewed Willow Nature source. Four material discrepancy candidates require governed correction before provenance can be attached without endorsing legacy wording. IN-001 incorrectly describes the 2021 repetition-code experiment as a surface-code implementation and confuses physical-qubit count with code distance: the experiment used repetition codes from d=3 to d=11, corresponding to 5 to 21 qubits, while the surface-code test was only d=2. IN-002 appears to conflate Quantinuum/Honeywell's 2021 real-time [[7,1,3]] colour-code QEC result with later fault-tolerant gate demonstrations; the 2021 experiment reported logical SPAM below physical SPAM but explicitly had not reached the overall error-correction threshold, so the present 2022 gate-level below-physical claim is not source-faithful as written. IN-003 overstates the 2023 Google Nature result: that experiment compared d=3 with d=5 on a 72-qubit device and achieved only a modest roughly 4% relative logical-error reduction, not d=3/d=5/d=7 with roughly halving at each step; d=7 and >2x suppression arrived with Willow. IN-004 misstates the Microsoft/Quantinuum 2024 result as approximately 10^-4 per two-qubit logical gate. The contemporaneous work reported circuit-level logical error reductions, including Bell-state preparation down to about 10^-5 with post-selection and repeated-error-correction comparisons, not a generic per-two-qubit-logical-gate 10^-4 metric; its broader claim that the result was below thresholds generally required for useful FTQC is also not directly established by that source. No historical wording, assessment, pressure state, verification stage, mechanism, lineage, or open question was silently changed. No verified experimental d=11+ below-threshold surface-code result was found. The 28 April 2026 Nature Author Correction to the Willow paper changes figure labelling only and does not alter the evidence interpretation. |
| M-012 | 2026-09-06 | Description restoreddescription_restored | Legacy ingestion cutoffs: mechanisms:RM-001, mechanisms:BN-001, mechanisms:AT-001, lineage:1995–96, lineage:1998–2012, lineage:2012–20 | Source-restored complete descriptionsWhat this update recorded for M-012Editorial Correction (GP-001), RENDER-PILOT-001 content restoration: restored RM-001, BN-001, AT-001; lineage 1995–96, 1998–2012, 2012–20 from FR_QE_0003_fault_tolerant_logical_qubits.html (Drive file 15wAwW5oDhl-eLUsK7g82KSR-0wJjufho). Each damaged value was a verified prefix of the recovered source after the existing FR-MF to FR-AM identifier migration. Restored the omitted remainder using the original converter text normalization; no inferred completion. Existing later corrections retained. Restoration recovers historical wording and does not reaffirm it as the current assessment. Assessments, evidence instances, open questions, claim, status and rendering eligibility unchanged. Source hashes and field receipt: docs/reviews/render-pilot-content-restoration.json; current-assessment compatibility review: docs/reviews/RENDER-PILOT-001-CONTENT-RESTORATION.md. |
| M-011 | 2026-07-08 | Experimental annotations retiredexperimental_annotations_retired | EXPERIMENTAL-ANNOTATIONS-ADDED | RETIREDWhat this update recorded for M-011Per Stuart's confirmation, the experimentalAnnotations[] pilot container (M-009) is retired and removed from this record. Its content is fully superseded by REN-001 (M-010), which formalises the same observation as a mature FCIF object. Removal carries zero migration cost, as documented in the pilot's own code comment (see FrontierRecord.jsx, record.experimentalAnnotations ?? []); no other record or component depends on this field. This is a deletion of pilot scaffolding, not an editorial correction under GP-001 and not a removal of assessments[] or other append-only evidentiary history. |
| M-010 | 2026-07-08 | Realization note addedrealization_note_added | — | REN-001What this update recorded for M-010realizationNotes field added to schema. REN-001 formalises, as a mature FCIF object, the same observation raised informally in the 2026-07-07 experimentalAnnotations pilot entry (M-009): evidentiary strengthening without corresponding realization progress. The experimentalAnnotations entry is left in place under append-only discipline and not deleted; its retirement, now that a mature schema field covers the same ground, is a decision for Stuart. Corpus Review — Realization Note Candidates (v2). |
| M-009 | 2026-07-07 | Experimental annotations addedexperimental_annotations_added | — | EXPERIMENTAL-ANNOTATIONS-ADDEDWhat this update recorded for M-009Added experimentalAnnotations[] — a pilot, non-schema-permanent container for editorial observations distinct from assessments[] and assessorNote. Status: experimental, under institutional review. Does not assert a pressureState or verificationStage change; assessments[] and its append-only history are untouched. First entry records that the claim's evidentiary trajectory is strengthening while realization-relevant enabling capabilities (per this record's own BN-001/RM-001) show no corresponding progress. The container and its rendering may be removed in a future release without migration if the pilot does not prove useful. |
| M-008 | 2026-07-03 | Reference correctionreference_corrected | — | REFERENCE-CORRECTEDWhat this update recorded for M-008Editorial Correction (GP-001): IN-004 and OQ-002 incorrectly cited FR-QE-0001 as containing evidence for Microsoft's topological qubit programme. FR-QE-0001 concerns Google Sycamore / random circuit sampling and contains no such content; the corpus currently has no dedicated Frontier Record for this programme. Corrected in both locations to state this accurately. IN-005's separate, correct reference to FR-QE-0001 (Willow's quantum-simulation instance) was reviewed and left unchanged. No evidence, interpretation, pressureState, verificationStage, assessment, or open question substance changed. |
| M-007 | 2026-06-28 | Assessment issuedassessment_issued | AS-001 | AS-002What this update recorded for M-007Evidence gap closed. IN-006 logged first; AS-002 issued second. Pressure state sustained as ESCALATING; verificationStage advanced VS-02 → VS-03. OQ-001 remains open because no d=11+ below-threshold result was verified. |
| M-006 | 2026-06-28 | Instance loggedinstance_logged | IN-005 | IN-006What this update recorded for M-006Willow below-threshold evidence reviewed as peer-reviewed surface-code memory result; d=11+ resolution bottleneck remains open. |
| M-005 | 2024-01-15 | Programme panel addedprogramme_panel_added | — | PROGRAMME-PANEL-ADDED |
| M-004 | 2024-01-15 | Mechanisms recordedmechanisms_recorded | — | MECHANISMS-RECORDED |
| M-003 | 2024-01-15 | Assessment issuedassessment_issued | — | ASSESSMENT-ISSUED |
| M-002 | 2024-01-15 | Instances loggedinstances_logged | — | INSTANCES-LOGGED |
| M-001 | 2024-01-15 | Record createdrecord_created | — | RECORD-CREATED |
Logged entries are reports on record, not counts of independent studies or patients. Several entries can concern the same underlying evidence. Supportive and Contesting describe an entry’s relation to the claim. Partial indicates limited or mixed bearing; read the details for limitations or legacy status. These labels are not study-quality ratings.
Correction pending: source review found a material discrepancy in this entry. Its legacy wording is retained pending a governed correction.
Google Quantum AI publishes in Nature (2021) demonstrating exponential suppression of one error type (bit-flip or phase-flip) as code distance increases in a surface code implementation on their Sycamore processor. They observe that logical error rates decrease as distance increases from d=5 to d=21 for one error type. The result does not yet demonstrate simultaneous suppression of both error types — full fault tolerance requires suppression of both — but it is the first published demonstration of the error-rate-versus-distance relationship the claim describes for a relevant error basis. The paper explicitly frames this as a necessary step toward fault tolerance rather than its achievement.
Correction pending: source review found a material discrepancy in this entry. Its legacy wording is retained pending a governed correction.
Quantinuum demonstrates high-fidelity logical qubit operations using a [[7,1,3]] Steane code on trapped-ion hardware, achieving logical error rates below physical error rates for specific gate operations. The result demonstrates that error correction overhead can be net-positive — that the logical qubit outperforms the physical qubits it is encoded across. The code distance tested is small; the experiment does not sweep code distance to demonstrate scaling behaviour. The result is supportive but does not directly measure the claim's specific empirical signature (improvement as distance increases). The hardware platform is distinct from Google's superconducting approach, indicating the phenomenon is not architecture-specific.
Correction pending: source review found a material discrepancy in this entry. Its legacy wording is retained pending a governed correction.
Google Quantum AI publishes in Nature (2023) the first demonstration of simultaneous suppression of both X and Z errors as surface code distance increases, from d=3 to d=5 to d=7, on a 72-qubit processor. Logical error rates decrease by approximately half with each increase in code distance. This is the specific empirical signature the claim describes: logical error rates improving as code distance increases, for a full surface code. The result is described by the authors as crossing the threshold from physical to logical error rate suppression. Independent commentary in Nature and Science acknowledges this as a qualitative milestone. The claim transitions from emerging to actively escalating pressure.
Correction pending: source review found a material discrepancy in this entry. Its legacy wording is retained pending a governed correction.
Microsoft and Quantinuum publish results demonstrating logical error rates of approximately 10⁻⁴ per two-qubit logical gate, achieved by combining Quantinuum's trapped-ion hardware with Microsoft's error correction software. The result achieves logical error rates orders of magnitude below physical rates and below thresholds generally cited as necessary for useful fault-tolerant computation. The result does not use topological qubits — it uses conventional trapped-ion hardware with software error correction. This is relevant to Microsoft's topological qubit programme — discussed as contextual evidence within the Quantum Engineering corpus but without a dedicated Frontier Record — which represents one pathway to fault tolerance; INST-004 demonstrates that fault-tolerant logical operation is achievable without it. The hardware-path question and the capability-threshold question are separable.
Shares the Willow publication with IN-006. Its later review entry does not establish an additional experiment. View IN-006
Google releases the Willow chip (105 qubits) and publishes results demonstrating below-threshold error correction: logical error rates decrease exponentially with code distance across d=3, d=5, and d=7 surface codes, with performance improving faster than the overhead of additional physical qubits. This is the first demonstration of below-threshold operation — the regime where adding more qubits to the code actively reduces logical error rates, making the system scalable in principle. Note: FR-QE-0001 logged the Willow chip's quantum simulation result as a separate instance relevant to the quantum advantage claim. The error correction result logged here is a distinct measurement from the same hardware, relevant to this record's specific claim.
Shares the Willow publication with IN-005. These entries discuss the same published result at different review points, not an additional experiment. View IN-005
The Willow below-threshold result is independently verifiable as a Nature/arXiv publication and materially strengthens the record's core empirical signature: the larger distance-7 logical memory suppresses error relative to distance-5, reaches approximately 0.143% error per cycle, and exceeds break-even against the best physical-qubit lifetime. The same evidence also defines the remaining constraint. The reported surface-code memories are still distance-5 and distance-7, with real-time decoding demonstrated at distance-5; the record's own OQ-001 asks whether below-threshold scaling holds at d=11 and above. No verified d=11+ below-threshold surface-code result was found in this review. This instance therefore supports sustained escalation but does not close the resolution bottleneck.