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.
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 evaluates whether a native constrained formulation, rather than a penalty-style QUBO conversion, helps D-Wave execution pathways recover fault-tree truth-objective solutions, using the locked 80-instance benchmark cohort from a prior platform-feasibility study (Paper 17), stratified into four problem-size groups of twenty instances each (16, 25, 33, and 42 Paper 17 QUBO variables). Two execution arms operate on the same cohort and the same frozen truth layer. Arm A is a direct-QPU pilot on a constraint-level QUBO (CL-QUBO)-derived penalty-style binary quadratic model (BQM). Arm B is a native constrained quadratic model (CQM) submitted to the D-Wave hybrid CQM solver, in which the fault-tree gate constraints are preserved as explicit constraints rather than compiled into penalties. The truth layer uses a minimum-cardinality criterion: an instance is truth-positive when a returned feasible sample matches the canonical truth objective. On the canonical eight-instance pilot, the direct-QPU Arm A recovered truth on 4 of 8 instances, with zero-truth behavior in the larger pilot strata, whereas the native hybrid CQM Arm B recovered truth on 8 of 8. Arm B recovery extended to a balanced twelve-instance set (12 of 12) and to the full locked cohort, recovering a truth-positive feasible solution on all 80 instances, with zero zero-truth instances and zero objective-below-truth anomalies, including 20 of 20 in every size stratum. This paper does not claim quantum advantage, computational speedup, or isolated QPU contribution within the hybrid solver; because the two arms differ in both formulation and pathway, it does not claim to isolate formulation as the sole causal factor. A retrospective timing audit of the preserved execution artifacts, performed without any resubmission, recovered complete solver timing metadata for all 88 jobs and found that two 16-variable instances were solved entirely by classical presolve with zero QPU access time, which bounds the interpretation of the full-cohort result without changing any recovery count. The results support semantic preservation as a central design requirement: the native constrained CQM pathway recovered the truth objective across the full cohort, while the penalty-style direct-QPU pilot showed size-limited recovery under the tested settings.
This paper evaluates D-Wave execution pathways for QUBO-based recovery of fault-tree minimum-cardinality cut sets using a balanced 80-instance benchmark cohort stratified into four problem-size groups of twenty instances each (16, 25, 33, and 42 QUBO variables). The experimental target is recovery of a minimum-cardinality cut set under a QUBO objective that minimizes the number of active basic events; the study does not enumerate the full minimal cut set family. Four execution arms operate on identical canonical payloads: a strict direct-QPU primary arm (Advantage2_system1, 1000 reads, 20 μs anneal time), a 5000-read direct-QPU replicate, a local classical simulated-annealing (SA) baseline at 1000 reads, and a hybrid BQM arm (LeapHybridSampler, 30 s). A deterministic fault-tree truth layer is used for per-sample validation; exhaustive QUBO ground-state enumeration via dimod.ExactSolver is performed only for the 16-variable stratum (20 of 20 confirmed), with the larger strata verified against deterministic fault-tree evaluation rather than exhaustive enumeration. Direct-QPU truth recovery degrades monotonically with problem size: zero-truth instance counts are 3, 10, 18, and 20 out of 20 under the 1000-read primary, and 0, 3, 11, and 19 under the 5000-read replicate. Classical SA at the same read budget recovers truth more often than direct QPU at every size (zero-truth counts 0, 1, 4, 13). Hybrid BQM recovered the canonical minimum-cardinality cut set on all 80 instances under the tested settings, including all 20 at 42 variables. This paper does not claim quantum advantage, computational speedup, replacement of classical cut-set algorithms, or full minimal-cut-set enumeration; it characterizes platform-level feasibility, minimum-cardinality correctness recovery, and size-stratified behavior across the four tested pathways. A device operation-timing analysis added in this revision shows that the fivefold read-budget increase corresponds to only a 4.18-fold increase in QPU access time, because programming is a fixed per-submission cost; it is reported as resource accounting and supports no time-to-solution, speedup, or cross-pathway equal-time claim.
Quadratic Unconstrained Binary Optimization (QUBO) formulations have been proposed as a pathway for applying quantum optimization algorithms to fault tree analysis. These formulations encode fault tree logic through penalty terms, converting constrained minimal cut set identification into unconstrained optimization. Prior work has demonstrated QUBO-MCS equivalence for small, carefully structured instances. This paper investigates whether penalty-based encodings of the type commonly used in the literature reliably preserve fault tree semantics at realistic problem scales when solved exactly. A cohort of 80 extended fault tree instances with OR, AND, and NOT gates was evaluated using two exact solvers: a constrained baseline that enforces fault tree semantics directly, and a branch-and-bound solver operating on soft QUBO formulations using Rosenberg product reductions. Even with the TOP event variable fixed, penalty coefficients conservatively scaled to exceed the maximum objective contribution, and exact (not heuristic) optimization, the soft QUBO solutions matched the constrained baseline in only 6 of 80 instances (7.5%). More critically, 22 of 80 instances (27.5%) produced solutions that violate fault tree gate semantics entirely. These results demonstrate that Rosenberg-based soft QUBO formulations with dominance-safe penalties do not reliably preserve fault tree semantics at scale under exact optimization, indicating a structural limitation of this class of unconstrained penalty encodings rather than a tuning deficiency. Complete experimental artifacts with SHA-256 verification are provided under the DOI above.
Cardinality-constrained portfolio selection is routinely cast as a quadratic unconstrained binary optimization (QUBO) and submitted to a quantum processing unit (QPU) for direct annealing. We show that this standard penalty encoding is the binding constraint for direct-QPU execution on current D-Wave Pegasus and Zephyr hardware. Expanding the exact cardinality penalty contributes a dense rank-one term that makes the logical interaction graph complete regardless of the covariance, producing chain-break fractions from 83% at small universes up to 92% at the full forty-nine-industry Fama--French universe, and zero feasible raw samples at every tested scale. Topology-aware sparsification reduces chain breaks to near zero, but any sparsifier that removes off-diagonal entries also dilutes the cardinality constraint; an ablation reveals that this sparsify-and-project pipeline is dominated by the classical projector, not the QPU. We propose removing the penalty entirely: sample an objective-only QUBO built from expected returns and the risk-scaled covariance on hardware, and enforce cardinality classically through a deterministic feasibility projector. Across 4,468 saved embedding records on live Pegasus and Zephyr hardware, spanning equities up to forty-nine assets and football-betting instances up to forty-eight, this penalty-free pipeline reduces mean chain-break fractions from 71%--92% down to at most 0.04%, and post-processed regret is at most 0.03% relative to greedy classical references at every tested scale. We do not claim quantum advantage; the penalty encoding, not the sparse hardware topology, is the limiting factor for direct-QPU portfolio optimization at currently accessible scales.
Quadratic Unconstrained Binary Optimization formulations for fault tree analysis encode gate logic through penalty terms, but prior work has demonstrated that these encodings fail to preserve fault tree semantics at scale: across 80 extended fault tree instances, only 7.5% of Rosenberg-based soft QUBO solutions match the constrained exact baseline, while 27.5% produce outright semantic violations. This paper develops two complementary methods to restore semantic correctness. A Hierarchical Semantic Validator and repair framework achieves 100% semantic validity across all 80 cohort instances through structure-aware bit-flip correction, improving the exact match rate from 7.5% to 28.75%. A constraint-level QUBO encoding eliminates penalty-based failures entirely by restricting optimization to the feasible subspace, reducing qubit requirements by a factor of 1.85x relative to Rosenberg encodings. Validation through Qiskit mixer circuits implementing a feasibility-preserving Quantum Alternating Operator Ansatz confirms zero probability leakage onto infeasible states for representative instances. These methods establish that semantic-preserving quantum optimization for fault tree minimal cut set identification is achievable with current algorithmic tools. Complete experimental artifacts with SHA-256 verification are provided under the DOI above.
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.