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PROG-QE
FR-QE-0007

Practical Quantum Advantage — Performance Beyond Classical Computation on Relevant Problems

A quantum computer has achieved quantum advantage on a practically relevant problem.

FragmentingVS-03·since 2026-09-17
Assessment trajectory
Fragmentingstate held · last assessed 2026-09-17
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
Current from 2024-01-15 — present
VS-04
Replication
—
VS-05
Operation
—
Stage first recorded Current verification position Not yet recorded
State Warrant
Current stateFragmentingVS-03
Why this state?Corrective assessment issued after LPR-001-D19. It supersedes provenance-dependent historical characterisations in AS-001/AS-002 without rewriting their append-only text. The IBM/University of Chicago 2026 hard-circuit result surfaced during LPR-001-D19 remains outside this correction pending Normal Record Review.
Assessment summaryLPR-001-D19 corrected the representation and provenance of IN-003, IN-004 and IN-006 without changing the claim's evidentiary state. IBM's 2023 utility experiment is now bounded to the classical approximations actually tested and its subsequent classical reproduction; Google's 2024 random-circuit-sampling evidence is separated from the distinct Willow surface-code result and company-reported benchmark estimates are explicitly attributed; and Quantum Echoes is represented as a programme in which reported beyond-classical performance and application relevance remain demonstrated at different scales. The corrected evidence continues to support FRAGMENTING / VS-03: strong performance evidence and meaningful application-oriented evidence exist, but no admitted instance yet establishes durable quantum advantage on a practically relevant problem at the same demonstrated scale.
State entered2024-01-15
Last reaffirmed2026-09-17
Mechanisms

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

BottleneckBN-001

"Practically relevant" lacks an agreed operational definition. The claim requires advantage on a practically relevant problem, but no agreed standard specifies what practical relevance requires. Different researchers and communities apply different implicit thresholds: some accept scientific relevance (the problem illuminates physical phenomena); others require commercial relevance (the result has identifiable downstream economic value); others require direct application (the computation produces output usable without further classical processing). Without agreement on this threshold, positive and contesting evidence cannot be cleanly compared — the Sycamore result is supportive under some definitions of relevance and irrelevant under others. This is the same threshold-dispute bottleneck as FR-BT-0001 BN-001 and FR-AM-0004 BN-001: not measurement validity, but an undefined success threshold.

Resistance MechanismRM-001

The best-classical comparison can improve materially after a quantum result is published. The IBM kicked-Ising episode provides a directly sourced example: a regime beyond brute-force computation and beyond the approximations tested in the original quantum study was subsequently reproduced by stronger tensor-network methods. This does not establish that classical methods will erase every proposed quantum advantage, but it means durability must be evaluated against the best method available for the specific problem at the time of comparison.

AttractorAT-001

First quantum computation on a practically relevant problem that establishes a durable advantage over the best contemporaneous classical method under a transparent comparison. A fault-tolerant quantum-chemistry calculation is one plausible route, but the record is not restricted to chemistry or to fault-tolerant hardware if another scientifically or commercially relevant problem satisfies both components at the demonstrated scale.

Assessment History
2024-01-15
Initial assessment — Fragmenting
The claim has not been satisfied. No quantum computer has demonstrated advantage on a problem that simultaneously meets both the performance threshold (faster than best classical methods) and the practical relevance threshold (problem has genuine scientific or commercial value at the demonstrated scale). The evidence base contains strong demonstrations of one component without the other — advantage on demonstration problems (INST-001, 002, 004) or near-advantage on relevant problems (INST-005) — but no instance yet satisfies both simultaneously. IBM's quantum utility claim (INST-003) comes closest to bridging the two, reporting results on a problem with some scientific relevance that classical simulation was disputed to match, but the classical-simulation contest remains unresolved. The pressure state is FRAGMENTING: the evidence is splitting along two separate trajectories — demonstration-problem advantage growing stronger (INST-004) and relevant-problem simulation approaching but not reaching classical intractability (INST-005) — without converging on a single instance that would resolve the claim (OQ-001).
Verification Stage: VS-03 preserved — historically unverified.
2026-08-28
Reassessed, no change — Fragmenting
Quantum Echoes materially narrows the gap between demonstration advantage and useful computation without satisfying the claim. IN-006 connects a reproducible higher-order OTOC result reported as approximately 13,000 times faster than the estimated classical computation with a concrete molecular-structure workflow using related OTOC measurements. The decisive conjunction remains absent: the beyond-classical result is demonstrated on large 65-qubit Quantum Echoes circuits, while practical utility is demonstrated on smaller molecular systems that do not themselves establish advantage over the best classical methods. The 2026 tensor-network analysis further supports the classical-intractability component but is produced by Google Quantum AI-affiliated authors and is not independent replication. The pressure state therefore remains FRAGMENTING: performance and relevance have moved closer within one technical programme but still occupy separate experimental regimes. Verification remains VS-03 because the central result is published and auditable, but neither independently replicated nor operationally demonstrated on a practically relevant beyond-classical task.
Bounded FR-QE-0007 impact review, 2026-08-28. Primary evidence: Google Quantum AI et al., Nature 646 (2025) 825–830, doi:10.1038/s41586-025-09526-6; Zhang et al., arXiv:2510.19550; Bermejo et al., arXiv:2604.15427. The Bermejo et al. follow-up is explicitly treated as Google-affiliated corroboration, not independent replication.
2026-09-17
Reassessed, no change — Fragmenting
LPR-001-D19 corrected the representation and provenance of IN-003, IN-004 and IN-006 without changing the claim's evidentiary state. IBM's 2023 utility experiment is now bounded to the classical approximations actually tested and its subsequent classical reproduction; Google's 2024 random-circuit-sampling evidence is separated from the distinct Willow surface-code result and company-reported benchmark estimates are explicitly attributed; and Quantum Echoes is represented as a programme in which reported beyond-classical performance and application relevance remain demonstrated at different scales. The corrected evidence continues to support FRAGMENTING / VS-03: strong performance evidence and meaningful application-oriented evidence exist, but no admitted instance yet establishes durable quantum advantage on a practically relevant problem at the same demonstrated scale.
Corrective assessment issued after LPR-001-D19. It supersedes provenance-dependent historical characterisations in AS-001/AS-002 without rewriting their append-only text. The IBM/University of Chicago 2026 hard-circuit result surfaced during LPR-001-D19 remains outside this correction pending Normal Record Review.
Claim Lineage

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

1994–2012
Theoretical quantum advantage established. Shor, Grover, and related algorithms prove that quantum computers can outperform classical computers on specific problems. The claim is theoretically established; hardware cannot yet demonstrate it.
2019
Google Sycamore — first "supremacy" claim. Advantage demonstrated on a demonstration problem; practical relevance contested. The claim enters the ESCALATING phase but the relevance component is immediately challenged.
2020–23
Repeated advantage demonstrations without practical relevance; NISQ-era utility claims. IBM's 2023 utility experiment adds scientific relevance but subsequent classical tensor-network reproduction shows that the beyond-classical comparison was not durable.
2024
Larger random-circuit-sampling experiments strengthen demonstration-problem performance claims, while the separate Willow surface-code result advances error correction. Neither establishes practical quantum advantage, and company-reported RCS runtime comparisons remain distinct from independently established bounds.
2025–26
Quantum Echoes brings reported beyond-classical OTOC performance and molecular-geometry application work into one technical programme, but the two components remain demonstrated at different scales and independent replication of the large-circuit advantage is absent.
Open Questions

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

OQ-001

Is there a problem type that is both classically intractable at demonstrated quantum scales and practically relevant? The two trajectories (demonstration advantage, relevant-problem simulation) need to converge on a single instance. Which specific problem will first satisfy both simultaneously?

Raised 2024-01-15
OQ-002

The attractor for FR-QE-0007 and FR-QE-0006 appears to be the same event: first fault-tolerant quantum chemistry calculation beyond classical reach. If both records resolve through the same instance, does the Observatory log it as one event serving two records, or two separate instances? The schema has no governed procedure for this.

Raised 2024-01-15
OQ-003

The null measurement validity condition held. Does this constitute sufficient evidence to characterise Measurement Validity as a proxy-measurement failure mode specifically, or does the two-occurrence positive evidence (FR-BT-0002, FR-AI-0007) plus one-occurrence negative evidence (FR-QE-0007) constitute a pattern worth a Review Note?

Raised 2024-01-15
Mutation Log
MutationDateFieldPrior valueCurrent value
M-0122026-09-17provenance_correctedLPR-001-D19 discrepanciesPASS-AFTER-CORRECTION
M-0112026-09-17provenance_review—LPR-001-D19 REVIEW REQUIRED
M-0102026-09-06description_restoredLegacy ingestion cutoffs: mechanisms:BN-001, mechanisms:RM-001, mechanisms:AT-001Source-restored complete descriptions
M-0092026-08-29provenance_enriched—PROVENANCE-ENRICHED
M-0082026-08-28reference_correctedIN-001–IN-005 lacked instance references; IN-005 misidentified Mi et al. as a superconducting-material phase-transition studyIN-001–IN-006 carry stable references; IN-005 reconstructed from Mi, Kandala and Yamamoto
M-0072026-08-28assessment_issuedAS-001AS-002
M-0062026-08-28instance_appendedIN-005IN-006
M-0052024-01-15programme_panel_added—PROGRAMME-PANEL-ADDED
M-0042024-01-15null_condition_met—NULL-CONDITION-MET
M-0032024-01-15assessment_issued—ASSESSMENT-ISSUED
M-0022024-01-15instances_logged—INSTANCES-LOGGED
M-0012024-01-15record_created—RECORD-CREATED
Evidence Sources
6 instances on recordShow sources ↓Hide ↑
IN-001Google Sycamore — "quantum supremacy" on random circuit sampling1. Arute et al., ‘Quantum supremacy using a programmable superconducting processor’, Nature 574, 505–510 (2019) DOI 10.1038/s41586-019-1666-5 · Abstract and main result2. Pednault et al., ‘Leveraging Secondary Storage to Simulate Deep 54-qubit Sycamore Circuits’ (2019)3. Pan, Chen & Zhang, ‘Solving the Sampling Problem of the Sycamore Quantum Circuits’, Physical Review Letters 129, 090502 (2022) DOI 10.1103/PhysRevLett.129.090502partial
IN-002Boson sampling experiments — photonic quantum advantage1. Zhong et al., ‘Quantum computational advantage using photons’, Science 370, 1460–1463 (2020) DOI 10.1126/science.abe87702. Madsen et al., ‘Quantum computational advantage with a programmable photonic processor’, Nature 606 (2022) DOI 10.1038/s41586-022-04725-xpartial
IN-003IBM quantum utility — kicked Ising model and subsequent classical simulation1. Kim, Y. et al. Evidence for the utility of quantum computing before fault tolerance. Nature 618, 500–505 (2023). DOI 10.1038/s41586-023-06096-3 · Abstract and classical-comparison discussion2. Tindall, J. et al. Efficient tensor network simulation of IBM's kicked Ising experiment. PRX Quantum 5, 010308 (2024). DOI 10.1103/PRXQuantum.5.010308 · Classical tensor-network reproduction and comparisonpartial
IN-004Google random-circuit sampling at larger scale — demonstration advantage without practical relevance1. Morvan, A. et al. Phase transitions in random circuit sampling. Nature 634, 328–333 (2024). DOI 10.1038/s41586-024-07998-6 · 67-qubit, 32-cycle random-circuit-sampling experiment and classical comparison2. Google Quantum AI. Meet Willow, our state-of-the-art quantum chip. 9 December 2024. · Company-reported RCS benchmark and classical-runtime estimate3. 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 · Separate Willow surface-code result; contextual distinction from RCSpartial
IN-005Quantum simulation of physical systems — approaching practical relevanceMi et al., Nature 601 (2022), doi:10.1038/s41586-021-04257-w; Kandala et al., Nature 549 (2017), doi:10.1038/nature23879; Yamamoto et al., Physical Review Research 4 (2022), doi:10.1103/PhysRevResearch.4.033110partial
IN-006Google Quantum Echoes and molecular-geometry OTOC programme1. Google Quantum AI and collaborators. Quantum echoes and the computational complexity of many-body dynamics. Nature 646, 825–830 (2025). DOI 10.1038/s41586-025-09526-6 · 65-qubit OTOC experiment and reported Frontier comparison2. Zhang et al. Molecular geometry from out-of-time-order correlators. arXiv:2510.19550 (2025). · Molecular distance and angle estimation using OTOCs3. Bermejo et al. Tensor-network analysis of Quantum Echoes circuits. arXiv:2604.15427 (2026). · Classical-simulation analysis; affiliated corroboration boundarypartial