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 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 whether feasible-subspace-preserving variational circuit families can compete with the frozen QAOA+ baseline from Peters (2026) for Constraint-Level QUBO (CL-QUBO) fault tree minimal cut set identification. Six alternative constructions—an independently parameterized XX+YY generator family, a cost-phase-augmented variant, a transpiled-matched variant, a structure-ordered variant, an n = 6 restricted screen, and a warm-start variant—were tested against the QAOA+ comparator on a frozen pilot cohort of 14 reactor-scale fault tree subtrees (10 n = 6, 4 n = 8a instances) under noiseless statevector simulation with deterministic multi-restart optimization. The directly materialized family constructions passed feasible-subspace closure audits, and the screen-only variants inherited closure-qualified source families. These audits confirmed that the excitation-number-conserving XX+YY construction remained inside the intended fixed-Hamming-weight sector for the tested CL-QUBO instances. The failure mechanism is identified through per-instance analysis: the alternative families concentrate essentially all statevector probability (≈99.99%) on a single computational basis state that does not correspond to a minimal cut set, while QAOA+ distributes probability across the feasible subspace with sufficient structure to place MCS among the highest-ranked outcomes. The independently parameterized generator family lacks the problem-specific cost–mixer alternation that gives QAOA+ its concentration advantage, and adding a single cost phase layer does not rescue this deficit. The result is a disciplined negative finding: within the tested family definitions and frozen screening protocol, no approved alternative produced evidence strong enough to justify hardware execution. The contribution is a careful narrowing of the viable variational design space for CL-QUBO fault tree optimization, establishing that feasible-subspace preservation alone is insufficient for competitive MCS enrichment. Complete experimental artifacts with SHA-256 verification are provided.
This paper presents a formal validation framework establishing equivalence between Quadratic Unconstrained Binary Optimization (QUBO) formulations and classical minimal cut set (MCS) identification for fault tree analysis in probabilistic risk assessment. The framework develops a 21-gate hierarchical verification system that proves QUBO ground states correspond exactly to minimal cut sets computed by the SCRAM fault tree solver. The validation methodology employs exhaustive enumeration for tractable models and conservative spot checks for larger instances, achieving PASS status across all verification gates. The theoretical contribution formalizes MCS identification as a constrained Boolean satisfiability problem amenable to quantum optimization. Fault trees with OR-of-ANDs structure are encoded into QUBO form with penalty terms enforcing logic constraints. The encoding preserves semantic equivalence: valid QUBO ground states map bijectively to classical minimal cut sets. Empirical validation demonstrates the framework on a canonical test case (TOP = A ∨ B ∨ (C ∧ D)) using QAOA simulation with plateau-based convergence methodology. The quantum circuit correctly identifies valid MCS configurations with p_opt = 0.01058 (95% CI: [0.00972, 0.01151]). Hardware feasibility is demonstrated through execution on IBM's ibm_torino 133-qubit Heron processor, where all circuits passed sanity and interpretation checks despite noise distributing probability across 110-120 unique states. The framework establishes foundational infrastructure for quantum PRA research by providing: (1) formal QUBO-MCS bijection verification against ground truth, (2) a reproducible classical baseline using the SCRAM solver, (3) plateau-based convergence criteria for stochastic quantum optimization, and (4) a hierarchical verification gate system ensuring scientific defensibility. No claim of quantum advantage is made; results are evaluated solely for semantic correctness, reproducibility, and NISQ feasibility.
Minimal cut set (MCS) identification is central to fault-tree-based probabilistic risk assessment (PRA), but quantum MCS methods have largely remained simulation-based or require Grover-style depths that are not executable on current hardware. This study reports an end-to-end IBM Quantum validation using shallow, fixed-parameter alternating-operator constraint-level QUBO (CL-QUBO) sampling circuits. The primary campaign executed 132 full-paired raw RL0 cells across 66 SCRAM-derived reactor fault-tree subtrees on two IBM devices, with 12 mapping-replicate controls held separate. Under an independently locked little-endian decoding convention, top-200 hardware outputs produced 2,596 exact-MCS state matches against 778 expected under a matched random-projection baseline, a 3.34× enrichment with 0.901 aggregate unique-MCS recovery. A 2,000-trial matched random-state null placed the all-campaign observed count outside the null distribution (empirical p < 5.0 × 10⁻⁴). Recovered cut sets preserved local PRA importance rankings with high fidelity, with mean Spearman correlations of 0.969 for Fussell-Vesely, 0.950 for Risk Reduction Worth, 0.934 for Birnbaum, and 0.920 for Risk Achievement Worth. A post-primary, pre-registered attribution ladder showed that removing the CL-QUBO cost phase collapsed the hardware result to the random/no-cost simulation scale (top-200 ratio 0.985), while the full p = 1 circuit remained at 3.34×. The results support cost-phase attribution for exact-MCS enrichment on current hardware, while making no claim of quantum advantage, plant-level risk quantification, or uniform behavior across all subtree classes.
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.
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.
This paper presents the first end-to-end evaluation of whether quantum-identified minimal cut sets (MCS) from physical IBM Quantum hardware can preserve standard probabilistic risk assessment (PRA) importance measures when compared against frozen SCRAM-validated classical baselines. It consumes frozen CL-QUBO hardware outputs from Paper 10 and propagates recovered MCS through two defensible probability-assignment tracks: a primary direct-component track based on NUREG/CR-6928 original component unreliability data and a secondary CCF extension track based on the 2020 NRC/INL common cause failure update using alpha factor methodology. Of 21 selected representative subtrees, 16 are promoted into the formal quantitative analysis set (10 primary, 6 extension), while five additional subtrees remain executed but quarantined in exploratory holdout lanes. Exact MCS recovery remains incomplete across both tracks. At the shared controlled operating point (ibm_marrakesh RL1 top-k = 10), the primary track achieves mean recovery fraction 0.225 with mean top-event absolute error 4.52 × 10⁻⁷, while the extension track achieves mean recovery fraction 0.292 with mean RAW Spearman 0.488, Birnbaum Spearman 0.438, FV Spearman 0.236, and mean top-event absolute error 7.50 × 10⁻⁷. Across the promoted set, tighter extraction windows generally outperform wider windows, set Jaccard is more informative than simple recovery fraction for downstream utility within this study, and the extension-track advantage survives common-support restriction but remains conditional and metric-dependent. The resulting pipeline therefore shows measurable but limited PRA utility: enough for screening-level assessment of relative component significance under favorable conditions, but not enough for standalone regulatory-grade quantification.