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 2024-01-15

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?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).

In this state since2024-01-15

Stage provenanceStored VS-04; historically unverified after legacy review.^*

Mechanisms

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

Resistance MechanismRM-001

Correlated error floors at large code distances. The threshold theorem assumes independent errors. Real systems contain correlated errors from crosstalk, cosmic ray impacts, and two-level system defects. At small code distances, these contribute minor corrections to the independent error model. At larger code distances, correlated errors may produce logical error rate floors — minimum achievable logical error rates that resist further suppression by adding physical qubits. The resistance mechanism is a potential breakdown of the theorem's assumptions at scales beyond the currently demonstrated range. The mechanism is real but its magnitude is not yet empirically established — no system has demonstrated a logical error rate floor in practice.

AttractorAT-001

Exponential suppression demonstrated through distance 11 or beyond. The claim would transition from RESOLVING to confirmed if exponential suppression is demonstrated at code distances 9 and 11 — the range required for early fault-tolerant applications. If suppression continues at these distances without evidence of correlated error floors, the claim's validity at practically relevant scales is established. Several hardware roadmaps (Google, IBM, Microsoft) project demonstrations at these distances within two to three years. The attractor is tractable and on a near-term engineering trajectory.

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.^*

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 exponential suppression at distance 3–5. First empirical confirmation that the scaling relationship holds in practice. The claim transitions from theoretical to empirical territory.

2024

Willow extends demonstration to distance 7; cross-platform confirmation. The scaling trajectory is confirmed across a wider range and across hardware platforms. Claim enters 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-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

5 instances on recordShow sources ↓Hide ↑

IN-001Threshold theorem — theoretical foundation establishedneutral

IN-002Google — exponential suppression demonstrated in distance-3 to distance-5 surface codessupportive

IN-003Google Willow — distance-3 to distance-7 scaling, below-threshold confirmedsupportive

IN-004Microsoft and Quantinuum — logical qubit operations at low error ratessupportive

IN-005Correlated errors and noise model limitations at larger scalespartial