FR-QE-0008

Quantum Error Correction Scaling — Logical Rate Suppression Under Physical Overhead

Quantum error correction can reduce logical error rates faster than physical error rates increase with system scale.

ResolvingVS-04·since 2026-09-18

Assessment trajectory

Resolvingstate held · last assessed 2026-09-18

Verification Matrix

Verification position derived from the record’s assessments; dates show when Faultline first recorded each stage.

VS-01

Assertion

—

VS-02

Published evidence

—

VS-03

Audit

—

VS-04

Replication

Current from 2024-01-15 — present

VS-05

Operation

—

Stage first recorded Current verification position Not yet recorded

State Warrant

Current stateResolvingVS-04

Why this state?Normal Record Review of Sivak et al., Nature 655 (2026), doi:10.1038/s41586-026-10759-2. Admitted as IN-006. No claim-resolution or verification-stage transition.

Assessment summaryIN-006 strengthens the operational scaling case by demonstrating that QEC syndrome information can continuously steer more than 1,000 control parameters during computation and materially improve logical stability against drift on Willow. This reduces one practical threat to maintaining below-threshold operation over long runtimes, but it does not extend the experimentally demonstrated surface-code distance beyond 7 and does not remove the correlated-error-floor evidence in IN-005. Simulated distance-15 scalability is supportive engineering evidence rather than an experimental scaling result. The claim therefore remains RESOLVING / VS-04: experimental logical-error suppression and active stabilization are both advancing, while durable scaling at application-relevant distances and runtimes remains unconfirmed.

State entered2024-01-15

Last reaffirmed2026-09-18

Mechanisms

Causal mechanisms recorded for this claim. The State Warrant above remains the authoritative current assessment.

Resistance MechanismRM-001

Correlated-error floors can limit logical-error suppression as code distance, physical overhead and runtime increase. Fault-tolerance threshold results depend on specified noise and decoding assumptions; they do not assert that all physical errors are independent. Real processors experience spatially or temporally correlated faults, including crosstalk, leakage and rare high-energy events. IN-005 documents measured floors in high-distance repetition codes: a distance-25 experiment exposed a 1.7×10⁻⁶-per-cycle floor set by a rare event, and Willow-generation tests reported an apparent floor around 10⁻¹⁰ at distance 15 and above from correlated bursts. Those are observed repetition-code effects, not evidence that Willow's distance-7 surface-code suppression has failed or that every architecture has the same floor. Whether such mechanisms can be mitigated over larger surface-code distances, longer runtimes and full fault-tolerant circuits remains unresolved.

AttractorAT-001

Sustained logical-error suppression as physical overhead and runtime increase on real hardware. Surface-code measurements at distances 9 and 11 would extend the established distance-7 evidence and directly test whether suppression persists beyond the current range, but those distances are neither universal requirements for useful fault-tolerant applications nor automatic confirmation of the broad claim. A resolution review would require reproducible scaling across an informative range of code sizes, correlated-error and long-runtime behaviour, and logical-operation and resource-overhead evidence at a practically relevant workload. Other code families must be judged by their own comparable scaling and resource metrics rather than surface-code distance numbers. A larger-distance result may strengthen the case without resolving correlated floors, full-circuit reliability or economics.

Assessment History

2024-01-15

Initial assessment — Resolving

The claim is substantially supported and on a trajectory toward confirmation. Google's Willow results (INST-003) demonstrate exponential logical error rate suppression through code distance 7, consistent with the threshold theorem's predictions. Cross-platform confirmation from Microsoft and Quantinuum (INST-004) strengthens the result beyond a single-platform observation. The core scaling relationship — logical error rates suppressing faster than physical overhead increases — is empirically confirmed at the code distances tested. The pressure state is RESOLVING: the theorem's central prediction has been consistently observed across the code distances measured so far (INST-002, INST-003) and across multiple hardware architectures, though correlated-error effects that may limit suppression at larger code distances (INST-005) have not yet been ruled out, and confirmation at the distances required for practical fault tolerance (d=9, d=11) remains the decisive open step (AT-001).

Verification Stage: VS-04 preserved — historically unverified.^*

2026-09-18

Reassessed, no change — Resolving

LPR-001-D20 correction preserves the substantive RESOLVING / VS-04 assessment while narrowing its evidentiary basis. Google's 2023 result established a modest distance-5-over-distance-3 logical improvement, and Willow later demonstrated below-threshold surface-code memories through distance 7 with Λ = 2.14 ± 0.02 per distance increase of two. Microsoft and Quantinuum provide separate trapped-ion evidence that logical encoding and correction can outperform corresponding physical circuit baselines, but not topological-hardware confirmation. Correlated-error floors are no longer hypothetical: Google observed measurable floors in high-distance repetition codes, including an apparent ~10⁻¹⁰ floor on Willow-generation hardware. The record therefore remains RESOLVING because below-threshold scaling is experimentally established over a growing range, while durability across larger code distances, long runtimes and full fault-tolerant circuits remains unresolved.

Corrective assessment following LPR-001-D20 bounded provenance repair. AS-001 is preserved append-only; IN-001 through IN-005 were source-bounded and representation errors corrected.

2026-09-18

Reassessed, no change — Resolving

IN-006 strengthens the operational scaling case by demonstrating that QEC syndrome information can continuously steer more than 1,000 control parameters during computation and materially improve logical stability against drift on Willow. This reduces one practical threat to maintaining below-threshold operation over long runtimes, but it does not extend the experimentally demonstrated surface-code distance beyond 7 and does not remove the correlated-error-floor evidence in IN-005. Simulated distance-15 scalability is supportive engineering evidence rather than an experimental scaling result. The claim therefore remains RESOLVING / VS-04: experimental logical-error suppression and active stabilization are both advancing, while durable scaling at application-relevant distances and runtimes remains unconfirmed.

Normal Record Review of Sivak et al., Nature 655 (2026), doi:10.1038/s41586-026-10759-2. Admitted as IN-006. No claim-resolution or verification-stage transition.

Claim Lineage

Historical narrative recorded for this claim. It does not override the current State Warrant.

1995–2012

Threshold theorem established; surface code identified. Theoretical foundation for scalable error correction is secure. The empirical question is whether physical systems satisfy the theorem's assumptions.

2022–23

Google demonstrates the first surface-code scaling break-even: the distance-5 code modestly outperforms the distance-3 ensemble on average. High-distance repetition-code tests also expose rare correlated-error floors.

2024–25

Willow demonstrates below-threshold surface-code memories through distance 7, with Λ≈2.14 per distance increase of two. Microsoft/Quantinuum provide separate trapped-ion logical-error reduction. Willow high-distance repetition codes reveal an apparent ~10⁻¹⁰ correlated-error floor. Claim remains RESOLVING.

Open Questions

Questions retained in this record. The current State Warrant may have narrowed or reframed earlier questions.

OQ-001

Does the distinction between independent sub-populations (PROG-AM) and hierarchical layers (PROG-QE) constitute a new observational category, or is it a refinement within the existing sub-population concept? The corpus has one occurrence of each type.

Raised 2024-01-15

OQ-002

If the substrate layer in PROG-QE resolves completely — if error correction scaling is confirmed at all practically relevant code distances — does the temporal displacement diagnosis change? A programme whose substrate is fully confirmed but whose applications remain decades away is in a different structural state than one whose substrate is still advancing.

Raised 2024-01-15

OQ-003

FR-QE-0004 and FR-QE-0008 are both RESOLVING substrate-layer records. If a third substrate-layer record enters RESOLVING, the substrate layer of PROG-QE would be functionally confirmed as a complete layer. Does that constitute a new kind of programme-level event — layer resolution — that the Observatory should track?

Raised 2024-01-15

Mutation Log

Mutation	Date	Field	Prior value	Current value
M-014	2026-10-03	instance_appended	IN-007	IN-008
M-013	2026-09-26	mechanism_attractor_consistency_corrected	RM-001 / AT-001 inherited absolute wording	Observed repetition-code floors and outcome-based scaling test
M-012	2026-09-26	instance_appended	IN-006	IN-007
M-011	2026-09-21	assessment_order_corrected	AS-003 → AS-002 → AS-001	AS-001 → AS-002 → AS-003
M-010	2026-09-18	instance_appended	IN-005	IN-006
M-009	2026-09-18	provenance_repair	LPR-001-D20 discrepancies_found / pending	LPR-001-D20 pass_after_correction / completed
M-008	2026-09-18	provenance_review	—	LPR-001-D20 REVIEW REQUIRED
M-007	2026-09-06	description_restored	Legacy ingestion cutoffs: mechanisms:RM-001, mechanisms:AT-001	Source-restored complete descriptions
M-006	2026-07-08	reference_corrected	—	REFERENCE-CORRECTED
M-005	2024-01-15	programme_panel_added	—	PROGRAMME-PANEL-ADDED
M-004	2024-01-15	sub_population_condition_partial	—	SUB-POPULATION-CONDITION-PARTIAL
M-003	2024-01-15	assessment_issued	—	ASSESSMENT-ISSUED
M-002	2024-01-15	instances_logged	—	INSTANCES-LOGGED
M-001	2024-01-15	record_created	—	RECORD-CREATED

Evidence Sources

8 instances on recordShow sources ↓Hide ↑

IN-001Threshold theorem and surface-code scaling — theoretical foundation1. Aharonov & Ben-Or, ‘Fault-Tolerant Quantum Computation with Constant Error Rate’, SIAM Journal on Computing 38 (2008) DOI 10.1137/S0097539799359385 · Abstract and threshold result2. Fowler et al., ‘Surface codes: Towards practical large-scale quantum computation’, Physical Review A 86, 032324 (2012) DOI 10.1103/PhysRevA.86.032324 · Surface-code architecture and fault-tolerance estimatesneutral

IN-002Google — distance-5 surface code modestly outperforms distance-31. Google Quantum AI, ‘Suppressing quantum errors by scaling a surface code logical qubit’, Nature 614, 676–681 (2023) DOI 10.1038/s41586-022-05434-1 · Abstract and logical error per cycle comparisonsupportive

IN-003Google Willow — below-threshold surface-code scaling through distance 71. Google Quantum AI and Collaborators, ‘Quantum error correction below the surface code threshold’, Nature 638, 920–926 (2025) DOI 10.1038/s41586-024-08449-y · Abstract; distance-5 and distance-7 scaling resultssupportive

IN-004Microsoft and Quantinuum — logical error reduction on trapped-ion hardware1. Microsoft, ‘Advancing science: Microsoft and Quantinuum demonstrate the most reliable logical qubits on record with an error rate 800x better than physical qubits’ (3 Apr 2024) · Four logical qubits; 800× comparison; active syndrome extraction2. Microsoft, ‘Microsoft announces the best performing logical qubits on record…’ (10 Sep 2024) · Twelve logical qubits and 22× circuit-error improvementsupportive

IN-005Correlated-error floors observed in high-distance repetition codes1. Google Quantum AI, ‘Suppressing quantum errors by scaling a surface code logical qubit’, Nature 614, 676–681 (2023) DOI 10.1038/s41586-022-05434-1 · Distance-25 repetition-code logical error floor2. Google Quantum AI and Collaborators, ‘Quantum error correction below the surface code threshold’, Nature 638, 920–926 (2025) DOI 10.1038/s41586-024-08449-y · High-distance repetition-code error floor and correlated-error budgetpartial

IN-006Google — reinforcement-learning control stabilizes QEC against drift1. Sivak et al., ‘Reinforcement learning control of quantum error correction’, Nature 655, 879–884 (2026) DOI 10.1038/s41586-026-10759-2 · Abstract, main results and Methods2. Google Quantum AI, data for ‘Reinforcement Learning Control of Quantum Error Correction’ (2026) DOI 10.5281/zenodo.18896801 · Experimental dataset; surface-code data collected 2026supportive

IN-007Quantinuum Helios — C4-Helix repeated correction and logical-operation benchmarks1. Berthusen et al., ‘Experimental validation of a compact fault-tolerant architecture for trapped ions’, arXiv:2609.03194v1 (2026) · Abstract; repeated QEC, logical-Clifford benchmark and chain-map interfacesupportive

IN-008Distributed surface-code lattice surgery — loss-tolerant fusion-network protocols1. Burt et al., ‘Loss-tolerant distributed lattice surgery using fusion networks’, arXiv:2610.01923v1 (2026) · Abstract; hybrid protocols, interface-erasure thresholds and local-noise simulationsneutral