FR-QE-0004

Below-Threshold Quantum Error Correction — Scalable Architecture

Quantum error correction can reduce logical error rates below physical error rates in a scalable architecture.

ResolvingVS-04·since 2024-01-15

Verification Matrix

VS-01

Assertion

—

VS-02

Published

—

VS-03

Audit

—

VS-04

Replication

2024-01-15 — present

VS-05

Operation

—

State reached Current state Not yet reached

State Warrant

Current stateResolvingVS-04

Why this state?The claim has two components: below-physical-rate operation, and scalability of that operation. Both have been demonstrated. INST-002 established that below-physical-rate logical qubits are achievable in principle. INST-003 established that practically useful error rates are achievable on current hardware. INST-004 established that performance improves as the architecture scales — the defining signature of scalable below-threshold operation. No contesting evidence has been published against either component of the claim. The pressure state is RESOLVING: both elements the claim requires have been independently demonstrated and corroborate each other, though confirmation at the code distances required for practical fault-tolerant computation (d=11 and above) remains outstanding (OQ-001), and the claim's architecture-agnosticism has not yet been confirmed across a third hardware platform (OQ-002).

In this state since2024-01-15

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

Mechanisms

Resistance MechanismRM-001

Physical qubit error floor at scale. Below-threshold operation at small code distances does not guarantee the behaviour continues as physical qubit count increases. Crosstalk, fabrication variability, and control complexity all tend to increase with system size. The resistance mechanism is not that below-threshold operation is unachievable — INST-004 demonstrates it is achievable — but that sustaining it as qubit count grows from hundreds to thousands to tens of thousands is an unsolved engineering problem. The claim as stated is in RESOLVING because the principle is established; this mechanism constrains how quickly the practical consequence follows.

AttractorAT-001

Demonstration at d=11 and beyond. The next decisive evidence event for this record is demonstration of below-threshold scaling at code distances d=11 and higher. At d=7, the Willow result establishes the behaviour. At d=11 or d=15, the result would confirm that the scaling continues into regimes relevant for practical fault-tolerant computation. This is the specific experimental milestone that would move the claim from RESOLVING toward a fully confirmed state. The attractor is clearly defined and the trajectory toward it is visible in current hardware development roadmaps.

Assessment History

2024-01-15

Record opened — Resolving

The claim has two components: below-physical-rate operation, and scalability of that operation. Both have been demonstrated. INST-002 established that below-physical-rate logical qubits are achievable in principle. INST-003 established that practically useful error rates are achievable on current hardware. INST-004 established that performance improves as the architecture scales — the defining signature of scalable below-threshold operation. No contesting evidence has been published against either component of the claim. The pressure state is RESOLVING: both elements the claim requires have been independently demonstrated and corroborate each other, though confirmation at the code distances required for practical fault-tolerant computation (d=11 and above) remains outstanding (OQ-001), and the claim's architecture-agnosticism has not yet been confirmed across a third hardware platform (OQ-002).

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

Claim Lineage

1995–97

Threshold theorem established. Aharonov, Ben-Or, Shor, and others prove that below-threshold physical error rates permit arbitrarily long fault-tolerant computation. The theoretical possibility of the claim is established. The empirical question opens: can physical hardware reach and sustain below-threshold operation?

1998–2019

Approach from above. Physical qubit error rates improve steadily across superconducting, trapped-ion, and photonic platforms. Surface code threshold (~1% two-qubit gate error) is approached but not consistently reached across full system operation. The claim remains in EMERGING state: the principle is sound, the hardware is insufficient.

2022–23

Threshold crossed at small scale. Quantinuum and the Microsoft/Quantinuum collaboration demonstrate below-physical-rate logical qubits and practically useful error rates. The claim enters ESCALATING. The scalability question becomes the active frontier.

2024

Scalable below-threshold operation demonstrated. Google Willow confirms that adding physical qubits to the code continues to reduce logical error rates — the defining signature of scalable below-threshold operation. The claim enters RESOLVING.

Open Questions

OQ-001

Does below-threshold scaling behaviour hold at code distances d=11 and above? This is the remaining decisive measurement before the claim can transition from RESOLVING to a fully confirmed state. AT-001 names this as the attractor.

Raised 2024-01-15

OQ-002

The claim is architecture-agnostic. Current evidence is concentrated in superconducting and trapped-ion systems. If topological qubit architectures — currently tracked only as contextual evidence within the corpus, without a dedicated Frontier Record — achieve confirmed below-threshold operation, this record gains a third platform confirmation. Does architecture-agnosticism require multi-platform demonstration, or is the current two-platform evidence sufficient for the claim as stated?

Raised 2024-01-15

OQ-003

What constitutes full confirmation of this claim — the transition from RESOLVING to a closed confirmed state? The corpus has no governed resolution criterion. The claim is precisely scoped and approaching resolution. Before another record reaches this point, the Observatory may need to address OQ-3 from FR-QE-0003: what does confirmation look like and who determines it?

Raised 2024-01-15

Mutation Log

Mutation	Date	Field	Prior value	Current value
M-011	2026-07-14	instances_appended	—	IN-007 / IN-008
M-010	2026-07-09	description_restored	—	DESCRIPTION-RESTORED
M-009	2026-07-09	description_reordered	—	DESCRIPTION-REORDERED
M-008	2026-07-03	reference_corrected	—	REFERENCE-CORRECTED
M-007	2026-07-03	instance_appended	—	INSTANCE-APPENDED
M-006	2024-01-15	programme_panel_added	—	PROGRAMME-PANEL-ADDED
M-005	2024-01-15	null_condition_met	—	NULL-CONDITION-MET
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

8 instances on recordShow sources ↓Hide ↑

IN-001Early surface code implementations — above-threshold operationneutral

IN-002Quantinuum — logical error rates below physical rates, small codesupportive

IN-003Microsoft / Quantinuum — logical error rates 10⁻⁴ per gatesupportive

IN-004Google Willow — below-threshold operation confirmed at multiple code distancessupportive

IN-005Multi-platform confirmation — Microsoft topological qubit announcementpartial

IN-006Legg et al. — peer-reviewed critique of topological gap detection; Microsoft responsecontesting

IN-007qLDPC breakeven on trapped-ion hardwareSUPPORTIVE

IN-008Real-time reinforcement-learning recalibration sustaining error-corrected operationSUPPORTIVE