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

Verification Matrix

VS-01

Assertion

—

VS-02

Published

2024-01-15

VS-03

Audit

2026-06-28 — present

VS-04

Replication

—

VS-05

Operation

—

State reached Current state Not yet reached

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

Record Lineage — Chronological

2024-01-15

Record opened — 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.

Mutation Log

Mutation	Date	Field	Prior value	Current value
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