Empirical scaling laws for the Quantum Approximate Optimization Algorithm (QAOA) on near-term hardware are often motivated by noise-compounding arguments or circuit-structure heuristics. Such models are rarely evaluated under pre-specified failure criteria that prevent post-hoc rescue. This study reports an audit-disciplined attempt to construct and test a predictive scaling law for QAOA-based minimal cut set recovery in fault tree models. The workflow used hash-locked artifacts, pre-specified kill switches, one-time holdout evaluation, and explicit no-rerun and no-rescue rules at every phase boundary. The initial F²-grounded compounding specification failed its pre-specified identifiability gate (KS3). Under an anti-leakage filter applied to 108 candidate rescue terms, zero candidates recovered a passing α₁ slope while also adding explanatory power above the structural baseline. A pre-specified structure-dominated fallback model was then defined and fit. The fallback reproduced its locked training prediction pathway to machine precision, with maximum absolute prediction difference of 3.55 × 10⁻¹⁵. It then failed the locked 24-row transport holdout. Holdout RMSE was 5.2214 against a locked threshold of 0.3770, and all 24 residuals were positive, giving a two-sided sign-test p-value of 1.19 × 10⁻⁷. The mean log residual of 5.198 corresponds to approximately 180-fold underprediction on the linear scale. Post-failure diagnostics indicated lower-n domain shift with standardized mean difference of −2.27 and four holdout rows with G_2q below the training range. By design, these diagnostics were explanatory only and did not authorize rescue, refit, reweighting, row removal, or threshold revision. The results do not support a deployable scaling law on the present corpus. Instead, they demonstrate that pre-specified audit controls can convert an attempted positive scaling-law claim into a reproducible falsification result with clear claim boundaries. The audit framework, the locked failure chain, and the allowed-and-forbidden claim boundary together constitute the paper's contribution. The work is offered as a methodological reference for future QAOA-on-hardware scaling studies.
Empirical scaling laws for the Quantum Approximate Optimization Algorithm (QAOA) on near-term hardware are often motivated by noise-compounding arguments or circuit-structure heuristics. Such models are rarely evaluated under pre-specified failure criteria that prevent post-hoc rescue. This study reports an audit-disciplined attempt to construct and test a predictive scaling law for QAOA-based minimal cut set recovery in fault tree models. The workflow used hash-locked artifacts, pre-specified kill switches, one-time holdout evaluation, and explicit no-rerun and no-rescue rules at every phase boundary. The initial F²-grounded compounding specification failed its pre-specified identifiability gate (KS3). Under an anti-leakage filter applied to 108 candidate rescue terms, zero candidates recovered a passing α₁ slope while also adding explanatory power above the structural baseline. A pre-specified structure-dominated fallback model was then defined and fit. The fallback reproduced its locked training prediction pathway to machine precision, with maximum absolute prediction difference of 3.55 × 10⁻¹⁵. It then failed the locked 24-row transport holdout. Holdout RMSE was 5.2214 against a locked threshold of 0.3770, and all 24 residuals were positive, giving a two-sided sign-test p-value of 1.19 × 10⁻⁷. The mean log residual of 5.198 corresponds to approximately 180-fold underprediction on the linear scale. Post-failure diagnostics indicated lower-n domain shift with standardized mean difference of −2.27 and four holdout rows with G_2q below the training range. By design, these diagnostics were explanatory only and did not authorize rescue, refit, reweighting, row removal, or threshold revision. The results do not support a deployable scaling law on the present corpus. Instead, they demonstrate that pre-specified audit controls can convert an attempted positive scaling-law claim into a reproducible falsification result with clear claim boundaries. The audit framework, the locked failure chain, and the allowed-and-forbidden claim boundary together constitute the paper's contribution. The work is offered as a methodological reference for future QAOA-on-hardware scaling studies.
This record contains a manuscript and supporting reproducibility materials for “Ledger-Valid Recovery Diagnostics for Quantum Computing: A Prespecified Sequential Audit for Claim-Limited Recovery Validation.” The paper proposes a methodological validation framework for quantum-computing recovery claims. Its central claim is that endpoint recovery success is necessary but not sufficient for a strong recovery claim when calibration failure, false-carrier acceptance, postselection artifacts, leakage, sentinel blindness, or hidden discard can carry failure modes out of view. The manuscript introduces a prespecified S0–S4 ledger audit that converts familiar diagnostic ingredients—label calibration, candidate recovery, false-carrier challenge tests, postselection/leakage accounting, and sentinel observability—into an ordered, claim-limiting taxonomy. A supportive recovery claim is permitted only when all required gates pass; otherwise, the first failed stage determines a lower claim ceiling and an interpretable failure class. The evaluation is based on synthetic endpoint-level validation suites rather than circuit-level simulation or hardware data. These suites test the behavior of the decision architecture under clean support, degraded observability, false-carrier artifacts, postselection/leakage artifacts, sentinel-blind cases, correlated artifacts, and adversarial overlap. The results show a strong specificity/sensitivity tradeoff: the full ledger protocol sharply reduces synthetic non-support supportive-call rates relative to endpoint-only reporting, but with substantial loss of mechanism-positive support sensitivity. The paper explicitly treats this as a conservative claim-validity architecture, not as a new quantum error-correcting code, new physical observable, hardware speedup, or proof of improved device performance. The supporting materials document the final synthetic validation protocol, endpoint definitions, decision-bound implementation, direction-aware threshold sensitivity analysis, latent-threshold eligibility analysis, mechanism-negative/latent-eligible boundary cases, and figure/table traceability. The archive is intended to support review of the manuscript’s aggregate numerical claims and methodological provenance. Hardware implementation, independent simulator validation, and full raw-event-ledger reproduction are identified as future extensions. Suggested keywords: quantum computing; quantum error correction; validation methodology; recovery diagnostics; leakage; postselection; benchmarking; synthetic validation; decision architecture; reproducibility.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for near-term quantum advantage in combinatorial optimization. A central design parameter is circuit depth p, with theoretical analyses suggesting higher p monotonically improves solution quality. This paper presents empirical evidence that this theoretical relationship does not hold on current noisy intermediate-scale quantum (NISQ) hardware for fault tree analysis applications. Across 120 QAOA executions on 60 QUBO-encoded fault tree instances (N ∈ {12, 16, 20, 24, 28, 32}) on IBM quantum hardware, circuit depths p = 1 and p = 2 were directly compared. The mean change in optimal state sampling probability from doubling circuit depth was Δmax_prob = 1.22 × 10⁻⁵ with a median Δ of zero, making the difference statistically indistinguishable from noise across all evaluated metrics. Output distribution entropy approaches the theoretical maximum (mean = 12.74 bits), indicating hardware noise dominates algorithmic signal. These findings establish that for fault tree minimal cut set identification on current NISQ devices, computational resources are more effectively allocated to increased shot counts than to circuit depth. Complete experimental artifacts with SHA-256 verification are provided, enabling full reproducibility.
This manuscript presents a methods-forward, operational protocol for evaluating whether any structured dependence remains in quantum-computing measurement records after explicit modeling of standard quantum and device-level mechanisms. Classical definiteness is defined at the record layer, and pre-record states are treated as predictive descriptions rather than as classical outcome facts. Within this operational stance, the protocol converts questions about outcome status and record formation into a falsifiable test program grounded in preregistered analysis rules and standard measurement telemetry. A locked null-model family is specified in advance, incorporating standard quantum dynamics together with documented device-level mechanisms including drift, correlated and non-Markovian noise, crosstalk proxies, and leakage indicators. The framework provides operational definitions, a conservative postulate set, preregistered endpoints, residual-adjudication criteria, negative controls, a fixed windowing discipline, and a bound-first reporting standard designed to yield informative constraints under null results. Any candidate contribution beyond the declared null family must appear as structured, reproducible residual dependence that survives the locked null family and the full residual-filter sequence. Version 4.4 refines the protocol specification, clarifies evidentiary boundaries, and strengthens the integration of the synthetic demonstration. The manuscript includes a fully specified classical simulation that executes the decision pipeline under controlled conditions. The synthetic study illustrates how the protocol classifies a bounded-null case, a measured-artifact case, a partial-artifact/unresolved-covariate case, an injected structured-residual case, and a failed-topology case. This demonstration establishes computational executability of the protocol and clarifies the behavior of the decision tree, but it does not constitute empirical evidence for any physical mechanism. Because the protocol relies only on standard measurement telemetry and preregistered analysis rules, it is directly implementable across contemporary quantum-computing platforms and does not depend on any single dataset, backend, or hardware realization. The manuscript is a specification paper: it defines a reproducible evidentiary framework for record-level claims, while large-scale empirical implementation, hardware benchmarking, and cross-platform replication remain subsequent studies.
Fault-tree analysis is a core component of probabilistic risk assessment (PRA), and quadratic unconstrained binary optimization (QUBO) provides a direct interface for evaluating fault-tree optimization problems on quantum annealers. A prior size-stratified study of an 80-instance fault-tree cohort observed sharp degradation in direct quantum-processing-unit (QPU) minimum-cardinality truth recovery as QUBO size increased, but the direct-QPU arms used a single anneal duration and did not isolate embedding, chain-strength, logical-variable relabelling, or chain-break explanations. This follow-on study prospectively pre-specified and SHA-256-locked a controlled robustness experiment on the same frozen penalty-QUBO cohort using D-Wave Advantage2 hardware. Eighty instances spanning 16, 25, 33, and 42 QUBO variables were evaluated across five forward-anneal durations and three deterministic fixed embeddings, with additional chain-strength controls on chained embeddings and four deterministic logical-variable relabelling diagnostics at 42 variables. The campaign completed 1,408 of 1,408 pre-specified conditions without execution or artifact failures and preserved 1,408,000 physical and 1,408,000 logical reads. Parameter selection affected recovery at smaller sizes: all 16- and 25-variable instances were truth-positive under at least one core condition. In contrast, only 18 of 20 33-variable instances and 3 of 20 42-variable instances were ever recovered across the fifteen anneal-time × embedding conditions, so 17 of 20 42-variable instances were never truth-positive. No tested anneal-time or chain-strength condition met the pre-specified material-rescue criterion, and four 42-variable relabelling diagnostics recovered zero instances. Only one of 1,408,000 logical reads exhibited a nonzero chain-break fraction, and that read was infeasible and not truth-positive. The results show size-dependent tuning leverage rather than parameter invariance: ordinary direct-QPU controls improve recovery within the smaller-size regime but do not materially rescue the large-size recovery frontier on this cohort and hardware epoch. Because the design fixes read count rather than QPU access time, anneal-duration comparisons are interpreted under equal read budgets rather than equal time. The study does not claim quantum advantage, universal formulation failure, full minimal-cut-set enumeration, or any time-to-solution or speedup result.
This paper presents a reproducible, audit-ready quantum hardware experiment for minimal cut set (MCS) inference on reactor fault tree subtrees using IBM Quantum hardware. Eight two-qubit subtrees were selected from a Phase 2B reactor-scale fault tree corpus spanning four nuclear hazard families (EQK, LOCA, TRANS, SGTR). Classical baselines were computed with SCRAM 0.16.2, yielding two order-1 MCS per instance. Shallow p = 1 Quantum Alternating Operator Ansatz (QAOA+) circuits were constructed using the Constraint-Level QUBO (CL-QUBO) encoding from Peters (2026b), transpiled to ibm_torino, and executed as batch jobs totaling 57,344 shots across four experiments. Raw hardware results showed apparent infeasible leakage of 13.2% on the hw = 0 state. A dedicated four-circuit readout calibration protocol revealed that this leakage was almost entirely attributable to readout error: after confusion-matrix correction (κ = 1.56), the baseline experiment concentrates 98.3% of probability mass on the MCS manifold (hw = 1), with residual infeasible mass of 0.5%. Extension experiments substantially broaden the empirical foundation. Cross-pair validation on three additional qubit pairs (ibm_torino pairs 61–62 and 36–48; ibm_marrakesh pair 6–7) confirms that corrected MCS fidelity exceeds 95% across all tested physical qubit assignments (range 95.2%–98.3%), with the best pairs achieving 98.2% (ibm_marrakesh 6–7) and 97.9% (ibm_torino 61–62). A QAOA depth sweep (p ∈ {1, 2, 3}) on ibm_torino pair 0–1 quantifies noise–depth tradeoffs: because the mixer is inactive (β = 0), the observed redistribution from hw = 2 toward hw = 1 (7.8% at p = 1, 25.6% at p = 2, 40.9% at p = 3) is attributable to gate noise rather than productive mixing, with infeasible hw = 0 mass rising concurrently from 0.2% to 7.2%. A three-qubit exactly-one constraint experiment on ibm_torino triple 0–1–2 achieves 92.2% corrected hw = 1 mass from a feasible initialization, demonstrating that the CL-QUBO framework extends beyond two-qubit OR gates to richer constraint types on quantum hardware. Hard-start initialization experiments confirm that p = 1 circuits do not induce sufficient mixing to recover MCS states from non-minimal initializations, with this conclusion stable across independent replication and all tested qubit pairs. Complete experimental artifacts with SHA-256 verification are provided under the DOI above.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for near-term quantum advantage in combinatorial optimization. A central design parameter is circuit depth p, with theoretical analyses establishing asymptotic convergence under idealized conditions. This paper presents a limits study demonstrating that this theoretical relationship does not translate to measurable improvement on current noisy intermediate-scale quantum (NISQ) hardware for fault tree analysis applications. Across 120 QAOA executions on 60 QUBO-encoded fault tree instances (N ∈ {12, 16, 20, 24, 28, 32}) on IBM Quantum hardware (ibm_torino, 133-qubit Heron processor), circuit depths p = 1 and p = 2 were directly compared. The mean change in optimal state sampling probability from doubling circuit depth was Δmax_prob = 1.22 × 10⁻⁵ with a median Δ of zero. For 8,192 shots, the binomial sampling uncertainty is O(10⁻²); the observed mean delta is therefore approximately three orders of magnitude below the shot-noise scale, making the difference statistically indistinguishable from zero. Output distribution entropy approaches the theoretical maximum of log₂(8192) ≈ 13 bits, indicating hardware noise dominates algorithmic signal. These findings establish that for fault tree minimal cut set identification on current NISQ devices, computational resources are more effectively allocated to increased shot counts than to circuit depth. Complete experimental artifacts with SHA-256 verification are provided, enabling full reproducibility.