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.
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.
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.
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 trees containing NOT logic can represent noncoherent structure functions, whose prime implicants may include or consist entirely of negated literals. A workflow that decodes candidate solutions as sets of positive basic events cannot express such an implicant at all, so the deficiency is representational rather than a shortfall of search effort. This paper asks whether a signed-literal constrained quadratic model can represent and retrieve that class, and what omitting it costs in downstream probabilistic risk assessment metrics. A complete De Morgan symbolic truth family was locked for a fixed 80-instance benchmark cohort before any signed-literal hybrid-solver submission in this study. Scoring existing positive-projection candidates against that authority left no unrecovered nonempty projection but isolated 99 all-negated signed implicants across 29 instances, for which existing artifacts supplied no hit. Those targets were preregistered, verified locally as minimal implicants, and encoded as a compact proof-tree model within 110 variables and 111 constraints per instance. Executed on a D-Wave Leap hybrid CQM solver with no target information supplied, the formulation returned exact signed-literal assignments for 73 of the 99 targets; preregistered target-conditioned submissions then closed the remaining cohort gaps at 99 of 99 exact and 99 of 99 superset under strict scoring, after an inflated earlier figure was corrected to 97 of 99. Over the complete state space the locked signed truth family reproduces the original Boolean function exactly, while a positive-only projection of it disagrees in every instance. The disagreement is directional: all 29 boundary instances carry false-negative states and underestimate the top-event probability for p at or below 0.1, whereas none of the 51 non-boundary comparison instances carries any. At an absolute sign tolerance of 1e-12, the exact model yields 855 resolved negative Birnbaum evaluations, whereas the positive-only surrogate yields none. No quantum advantage, speedup, isolated QPU contribution, family enumeration, or plant-specific risk estimate is claimed.
This paper presents an audit-ready benchmark, comparison, and freeze decision for alternative CL-QUBO builder and variational family paths applied to fault tree minimal cut set (MCS) identification. The study evaluates whether cost-phase-augmented variational families from prior work can challenge the incumbent CL-QUBO builder path (v5) on a widened 9-case tiny validation corpus covering OR, AND, NOT, and nested gate structures. A disciplined promotion pipeline, comprising role mapping, contract extraction, execution coverage adjudication, semantic grid screening across 1,305 parameter configurations, and formal synthesis, was exercised to ensure that challengers were genuinely advanced rather than dismissed prematurely. Two evidence tiers structure the comparison: the incumbent v5 was evaluated through exact combinatorial audit (exhaustive projected-MCS-family recovery), while challengers were evaluated through best-of-grid statevector screening (top-1 MCS family membership and total MCS mass). The incumbent v5 achieved 9 of 9 primary target hits (minimum-cardinality MCS under the minimize-basic-events objective) and 8 of 9 exact all-MCS family recovery hits, with the single miss occurring on a case where the minimum-cardinality MCS is a strict subset of the full MCS family. The independent cost-phase challenger achieved 3 of 9 primary hits and 3 of 9 all-MCS top-1 hits at best-of-grid. The block-shared cost-phase challenger achieved 3 of 8 primary and 3 of 8 all-MCS top-1 hits on applicable cases, with one case (TVC_007_NOT_A) structurally not applicable because the block-shared generator schedule requires a retained prefix structure that the one-qubit case does not provide. The completion gate passed all eight checks, and v5 was frozen as the final promoted path within the widened tiny benchmark scope studied. This paper does not claim quantum advantage.
This paper evaluates quantum recovery of minimal cut set (MCS) structure across eight IBM hardware runs spanning four runtime arms (A1–A4) and two backends (ibm_torino and ibm_marrakesh), using an independent raw-counts recomputation as the authoritative analysis layer. Each arm combines a resilience level (RL0, RL1, or RL2) with a dynamical decoupling (DD) setting (on or off), applied to CL-QUBO fault tree circuits encoding 8 reactor-scale pilot subtrees from a prior hardware study. Each run submitted 8 primitive unified blocs (pubs), one per subtree, at 8,192 shots each with bind parameters [0.2, 0.2]. The canonical analysis spans 64 pubs and 12,800 top-200 rows with zero unresolved issues. The principal finding is that the IBM hardware runs produced nonzero exact and nonzero superset MCS recovery. Across the study, mean top-200 exact hits were 16.6 per pub (range 10.4–22.6 across runs), mean exact MCS mass was 0.074, mean exact-or-superset mass was 0.820, and mean superset-nonexact mass was 0.746. Recovery is present but is not dominated by exact MCS outcomes: approximately 91% of the recovered exact-or-superset probability mass lies in superset-nonexact structure. ibm_torino showed descriptively stronger exact recovery (mean exact hits 20.8 versus 12.5 for ibm_marrakesh), while ibm_marrakesh showed descriptively stronger broad superset-heavy recovery (mean superset hits 146.4 versus 134.3 for ibm_torino). An earlier scorer-layer analysis yielded a zero-recovery interpretation; the independent raw-counts recomputation showed that this was an artifact of a contract mismatch and supersedes the earlier result. This paper does not claim quantum advantage.
Hybrid quantum-classical solvers conceal how reported performance divides between quantum-processing-unit (QPU) access and other service time. We audit D-Wave's Leap service on cardinality-constrained mean-variance portfolio instances from N=10 to 640, comparing constraint-native CQMs, penalty-encoded BQMs, Gurobi MIQP, simulated annealing, and a matched-budget Tabu baseline, and we propose a four-metric operational audit of the exposed timing fields. LeapHybridCQM matches Gurobi's proven optimum on all 54 head-to-head instances at N<=120, yet its mean QPU access is 0.034 s: 0.68% of the nominal five-second budget; telemetry does not resolve the residual into classical computation, orchestration, or budget granularity. Across 108 fixed-seed five-second CPU runs on 36 instances, TabuSampler reaches CQM-level objectives with mean absolute delta 0.00078 (maximum 0.00798); at N in {400,640} the mean is 3.04e-5. This establishes classical objective achievability, not an internal QPU ablation. We prove that quadratic encoding of exact cardinality adds a dense rank-one term and, apart from isolated exact coefficient cancellations, yields a complete logical graph independent of covariance support, with a bounded-degree embedding lower bound; the resulting density collapse is consistent with hybrid-BQM degradation. A descriptive five-window Fama-French overlay of post-projection direct-QPU portfolios yields mean Sharpe 1.94 versus 2.22 for 1/N. These results do not establish a quantum-sampling advantage; they motivate reporting QPU wall-clock fraction, optimality gap, density amplification, service-output variance, and matched-budget classical controls, keeping operational accounting separate from causal attribution.