FR-QE-0003

Fault-Tolerant Logical Qubits — Error Rate Scaling with Code Distance

Fault-tolerant logical qubits can be demonstrated with logical error rates that improve as error-correcting code distance increases.

EscalatingVS-03·since 2026-06-28

Assessment trajectory

Escalatingstate held · last assessed 2026-06-28

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

First recorded 2024-01-15

VS-03

Audit

Current from 2026-06-28 — present

VS-04

Replication

—

VS-05

Operation

—

Stage first recorded Current verification position Not yet recorded

State Warrant

Current stateEscalatingVS-03

Why this state?Assessment filed after direct review of FR-QE-0003 and current external sources on 2026-06-28. The new assessment references only IN-006 evidence already logged in this record. No existing instance, mechanism, open question, or prior assessment was modified. No transition is forced: IN-006 strengthens the claim and advances verification, but it does not satisfy OQ-001 or define the governed RESOLVING criterion requested by OQ-003.

Assessment summaryThe evidence gap is closed by IN-006. The Willow result is now treated as a verified, peer-reviewed below-threshold surface-code memory result rather than a general quantum-computing announcement. It materially strengthens the claim because logical error suppression improves with code distance and the larger memory exceeds break-even. The pressure state remains ESCALATING rather than RESOLVING because the record's own next decisive question — whether below-threshold scaling holds at d=11 and above — remains unanswered, and the demonstrated result is still a memory result rather than a full fault-tolerant computation pathway.

State entered2024-01-15

Last reaffirmed2026-06-28

Mechanisms

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

Resistance MechanismRM-001

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.

BottleneckBN-001

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.

AttractorAT-001

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 constitute resolution of the claim as stated. 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.

Assessment History

2024-01-15

Initial assessment — Escalating

The claim describes a specific empirical signature: logical error rates improving as code distance increases. This signature has now been demonstrated. INST-003 (Google, 2023) was the first result to show simultaneous X and Z error suppression with increasing code distance, directly satisfying the claim's measurement criterion. INST-005 (Google Willow, 2024) extends this to below-threshold operation, showing that the improvement rate exceeds the overhead rate — the condition required for the result to be considered scalable rather than merely demonstrated at fixed size. INST-001 (2021) and INST-002 (2022) provided earlier partial evidence — single-error-type suppression and below-physical-error-rate operation, respectively — establishing the trajectory that INST-003 and INST-005 confirm more directly. The pressure state is ESCALATING: the claim's core empirical signature is demonstrated and strengthening, but the demonstrated code distances (up to 7) remain well below the distances required to confirm the behaviour holds at practically relevant scale (OQ-001).

Verification Stage: VS-02 preserved — historically unverified.^*

2026-06-28

Reassessed, no change — Escalating

The evidence gap is closed by IN-006. The Willow result is now treated as a verified, peer-reviewed below-threshold surface-code memory result rather than a general quantum-computing announcement. It materially strengthens the claim because logical error suppression improves with code distance and the larger memory exceeds break-even. The pressure state remains ESCALATING rather than RESOLVING because the record's own next decisive question — whether below-threshold scaling holds at d=11 and above — remains unanswered, and the demonstrated result is still a memory result rather than a full fault-tolerant computation pathway.

Assessment filed after direct review of FR-QE-0003 and current external sources on 2026-06-28. The new assessment references only IN-006 evidence already logged in this record. No existing instance, mechanism, open question, or prior assessment was modified. No transition is forced: IN-006 strengthens the claim and advances verification, but it does not satisfy OQ-001 or define the governed RESOLVING criterion requested by OQ-003.

Claim Lineage

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

1995–96

Fault tolerance theory established. Shor (1995) and Steane (1996) independently propose quantum error correcting codes. Aharonov and Ben-Or (1997) prove the threshold theorem: if physical error rates are below a threshold, arbitrarily long quantum computation is possible. The claim becomes theoretically well-founded; the empirical question becomes whether physical systems can reach and stay below threshold.

1998–2012

Small-scale demonstrations. Multiple groups demonstrate quantum error detection and correction in small systems (2–7 qubits) across NMR, trapped ion, and photonic platforms. Error rates are above threshold; demonstrations are proof-of-principle rather than performance milestones. The claim is in an EMERGING state throughout this period.

2012–20

Superconducting qubit scaling. Google, IBM, and others scale superconducting systems to tens of qubits. Physical error rates approach but do not consistently reach below-threshold operation. The engineering challenge shifts from demonstrating error correction to demonstrating that adding qubits helps rather than hurts.

2021–23

Distance scaling demonstrated. Google's 2021 and 2023 Nature papers establish the specific empirical signature. The transition from partial (one error type) to full (both error types) suppression with distance marks the transition from EMERGING to ESCALATING for this record.

2024

Below-threshold operation and multi-platform confirmation. Google Willow and Microsoft/Quantinuum results establish below-threshold operation and demonstrate the phenomenon across multiple hardware platforms. The claim is in its strongest evidential state to date.

Open Questions

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

OQ-001

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.

Raised 2024-01-15

OQ-002

The 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?

Raised 2024-01-15

OQ-003

The 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.

Raised 2024-01-15

Mutation Log

Mutation	Date	Field	Prior value	Current value
M-012	2026-09-06	description_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 descriptions
M-011	2026-07-08	experimental_annotations_retired	EXPERIMENTAL-ANNOTATIONS-ADDED	RETIRED
M-010	2026-07-08	realization_note_added	—	REN-001
M-009	2026-07-07	experimental_annotations_added	—	EXPERIMENTAL-ANNOTATIONS-ADDED
M-008	2026-07-03	reference_corrected	—	REFERENCE-CORRECTED
M-007	2026-06-28	assessment_issued	AS-001	AS-002
M-006	2026-06-28	instance_logged	IN-005	IN-006
M-005	2024-01-15	programme_panel_added	—	PROGRAMME-PANEL-ADDED
M-004	2024-01-15	mechanisms_recorded	—	MECHANISMS-RECORDED
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

6 instances on recordShow sources ↓Hide ↑

IN-001Google — Exponential suppression of bit or phase errors with cyclic error correctionsupportive

IN-002Quantinuum — fault-tolerant logical qubit operations on trapped-ion hardwaresupportive

IN-003Google — Suppressing quantum errors by scaling a surface code logical qubitsupportive

IN-004Microsoft / Quantinuum — logical qubit error rates below 10⁻⁴ per gatesupportive

IN-005Google Willow — below-threshold quantum error correction at scalesupportive

IN-006Google Willow — peer-reviewed below-threshold result leaves d=11+ unresolvedsupportive