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PROG-QE
FR-QE-0006

Fault-Tolerant Quantum Utility — Practically Useful Algorithms Beyond Classical Simulation

A fault-tolerant quantum computer can execute a practically useful quantum algorithm beyond classical simulation.

EscalatingVS-02·since 2026-09-16
Assessment trajectory
Escalatingstate held · last assessed 2026-09-16
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
Current from 2024-01-15 — present
VS-03
Audit
—
VS-04
Replication
—
VS-05
Operation
—
Stage first recorded Current verification position Not yet recorded
State Warrant
Current stateEscalatingVS-02
Why this state?Normal Record Review of Proctor et al., arXiv:2609.12146. QUOPS is admitted as supportive gap-measurement evidence, not as a utility demonstration. Its application translations and future projections remain model-dependent and peer review is pending.
Assessment summaryIN-007 adds a system-level bridge between present processor capability and recognised utility-scale workloads. QUOPS experimentally benchmarks physical processors and a small fault-tolerant logical processor, then translates FeMoco and RSA-2048 resource estimates into the same circuit-capability framework. For this record, the important result is that the FeMoco-class target remains roughly five orders of magnitude beyond present measured circuit-size capability despite measurable logical-computation progress. This strengthens the evidence that the engineering path can be measured coherently while simultaneously showing that practical utility has not been reached. The claim remains unsatisfied; Pressure State remains ESCALATING and Verification Stage remains VS-02.
State entered2024-01-15
Last reaffirmed2026-09-16
Mechanisms

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

Resistance MechanismRM-001

Classical comparison methods improve alongside quantum hardware. A claim of utility must be tested against the best classical method available for the specific problem at the time. QUOPS adds a system-level quantum capability measure but does not remove the need for an application-specific classical comparator.

BottleneckBN-001

No demonstrated end-to-end fault-tolerant application at useful scale. Candidate chemistry problems such as FeMoco have concrete but architecture-dependent resource estimates. QUOPS now provides a common circuit-capability framework linking measured processors to such targets, but its FeMoco translation still places the target roughly five orders of magnitude beyond present measured circuit-size capability. Claim satisfaction requires a useful problem, a fault-tolerant implementation at required scale and depth, and a contemporaneous best-classical comparator.

AttractorAT-001

First end-to-end fault-tolerant computation on a practically useful problem that remains beyond the best classical method under a transparent contemporaneous comparison. FeMoco-class chemistry is one candidate. QUOPS can provide an additional system-level capability measure on the route to this event, but no benchmark score or fixed logical-qubit count is itself sufficient: the decisive event remains useful computation plus durable classical separation.

Assessment History
2024-01-15
Initial assessment — Escalating
The claim has not been satisfied. No fault-tolerant quantum computer has executed a practically useful quantum algorithm beyond classical simulation at the scale required for genuine practical advantage. The substrate progress (INST-003) establishes that fault-tolerant logical qubits capable of executing simple circuits now exist; the resource estimation (INST-004) establishes a large application-scale gap. Classical simulation methods are simultaneously improving. The pressure state is ESCALATING: the substrate is advancing on a credible path, but no agreed target problem yet exists.
Verification Stage: VS-02 preserved — historically unverified.
2026-08-17
Reassessed, no change — Escalating
The claim remains unsatisfied and ESCALATING. IN-006 advances the fault-tolerant substrate beyond protected logical memory by demonstrating composed logical Clifford operations through lattice surgery on a superconducting surface-code processor. That is a real engineering advance, but it does not cross this record's load-bearing boundary: the demonstration is Clifford-only, uses distance-three codes, supplies no practically useful target problem, and does not establish execution beyond the best classical simulation.
Issued during OHR-2026-09 catch-up review to close the evidence-assessment gap created by IN-006.
2026-09-16
Reassessed, no change — Escalating
LPR-001-D18 corrected the provenance and representation of IN-001 through IN-005 without altering the underlying claim. The corrected evidence continues to support ESCALATING / VS-02: the engineering path is credible and advancing, but no fault-tolerant system has executed a practically useful algorithm beyond the best classical simulation.
Corrective assessment issued after LPR-001-D18. It supersedes provenance-dependent historical characterisations without rewriting their append-only text.
2026-09-16
Reassessed, no change — Escalating
IN-007 adds a system-level bridge between present processor capability and recognised utility-scale workloads. QUOPS experimentally benchmarks physical processors and a small fault-tolerant logical processor, then translates FeMoco and RSA-2048 resource estimates into the same circuit-capability framework. For this record, the important result is that the FeMoco-class target remains roughly five orders of magnitude beyond present measured circuit-size capability despite measurable logical-computation progress. This strengthens the evidence that the engineering path can be measured coherently while simultaneously showing that practical utility has not been reached. The claim remains unsatisfied; Pressure State remains ESCALATING and Verification Stage remains VS-02.
Normal Record Review of Proctor et al., arXiv:2609.12146. QUOPS is admitted as supportive gap-measurement evidence, not as a utility demonstration. Its application translations and future projections remain model-dependent and peer review is pending.
Claim Lineage

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

1994–2009
Shor, Grover and HHL establish important theoretical quantum speedups under problem-specific assumptions; practical utility remains contingent on implementation and end-to-end resource costs.
2020–21
Lee et al. quantify a representative FeMoco fault-tolerant workload at 2,142 logical qubits and billions of Toffoli gates, illustrating the application-scale resource gap without defining a universal threshold.
2023–24
IBM's pre-fault-tolerant utility experiment is followed by stronger classical tensor-network simulation, demonstrating that the beyond-classical comparison boundary can move.
2024–25
Small-scale logical error suppression strengthens the fault-tolerant substrate, but does not demonstrate a useful algorithm or a generic logical-gate error/depth threshold.
2026
Composed logical operations advance the active fault-tolerant substrate. QUOPS then supplies a common system-level benchmark spanning physical processors, a small logical processor and utility-scale challenge translations; its FeMoco mapping places present measured circuit-size capability about five orders of magnitude below the target.
Open Questions

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

OQ-001

Which specific molecular or physical system will provide the first unambiguous fault-tolerant quantum advantage? Whether the first advantage demonstration will be accepted as practically useful depends on the problem solved and the contemporaneous classical comparator.

Raised 2024-01-15
OQ-002

Does the PROG-QE diagnosis — technically coherent but temporally displaced — create investment sustainability risk? If investment cycles shorten before applications arrive, the substrate may stop advancing before the claim is satisfied.

Raised 2024-01-15
OQ-003

Are the programme diagnosis types a property of the domains, or of the specific claim configurations the Observatory selected?

Raised 2024-01-15
Mutation Log
MutationDateFieldPrior valueCurrent value
M-0142026-09-16record_reviewLPR-001-D18 Record Review candidateIN-007 / AS-004
M-0132026-09-16provenance_correctedLPR-001-D18 discrepanciesPASS-AFTER-CORRECTION
M-0122026-09-16provenance_review—LPR-001-D18 REVIEW REQUIRED
M-0112026-09-06description_restoredLegacy ingestion cutoffsSource-restored complete descriptions
M-0102026-08-17assessment_issuedAS-001AS-002
M-0092026-07-14instance_appended—IN-006
M-0082026-07-08reference_corrected—REFERENCE-CORRECTED
M-0072026-07-08realization_note_added—REN-001
M-0062024-01-15programme_panel_added—PROGRAMME-PANEL-ADDED
M-0052024-01-15null_condition_failed—NULL-CONDITION-FAILED
M-0042024-01-15mechanisms_recorded—MECHANISMS-RECORDED
M-0032024-01-15assessment_issued—ASSESSMENT-ISSUED
M-0022024-01-15instances_logged—INSTANCES-LOGGED
M-0012024-01-15record_created—RECORD-CREATED
Evidence Sources
7 instances on recordShow sources ↓Hide ↑
IN-001Quantum algorithm portfolio — theoretical speedups established1. Shor, P. W. Algorithms for quantum computation: discrete logarithms and factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science (1994). DOI 10.1109/SFCS.1994.365700 · Algorithm and complexity result2. Grover, L. K. A fast quantum mechanical algorithm for database search. Proceedings of STOC '96 (1996). DOI 10.1145/237814.237866 · Search algorithm and query complexity3. Harrow, A. W., Hassidim, A. & Lloyd, S. Quantum algorithm for linear systems of equations. Physical Review Letters 103, 150502 (2009). DOI 10.1103/PhysRevLett.103.150502 · Abstract and stated assumptionsneutral
IN-002IBM quantum-utility experiment — classical boundary subsequently contested1. 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. arXiv:2306.14887 (2023). · Abstract and simulation comparisonpartial
IN-003Logical error suppression — fault-tolerant substrate advances without useful-algorithm demonstration1. 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 · Published online 9 December 2024; increasing-distance surface-code result2. Quantinuum and Microsoft. Breakthrough demonstration of reliable logical qubits. 3 April 2024. · Company announcement; four logical qubits and circuit-level error suppressionsupportive
IN-004FeMoco resource estimate — application-scale fault tolerance remains demanding1. Lee, J. et al. Even more efficient quantum computations of chemistry through tensor hypercontraction. PRX Quantum 2, 030305 (2021). DOI 10.1103/PRXQuantum.2.030305 · FeMoco resource estimates and fault-tolerant implementation analysispartial
IN-005Classical simulation improvement — comparison boundary moves1. 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 · Original quantum experiment and tested classical approximations2. Tindall, J. et al. Efficient tensor network simulation of IBM's kicked Ising experiment. arXiv:2306.14887 (2023). · Classical tensor-network simulation resultcontesting
IN-006Composed logical Clifford operations via lattice surgery on a superconducting surface-code processor1. Lin, W. et al. Surface code logical operations on a superconducting quantum processor. arXiv:2607.01473 (2026). DOI 10.48550/arXiv.2607.01473 · Abstract; submitted 1 July 2026NEUTRAL
IN-007QUOPS benchmark — measured computational capability mapped to utility-scale challenge workloads1. Proctor, T. et al. Benchmarking the computational power of quantum computers. arXiv:2609.12146 (2026). DOI 10.48550/arXiv.2609.12146 · Abstract; QUOPS physical/logical measurements and challenge-problem resource translation; submitted 10 September 2026supportive