This paper presents a standalone, audit-ready pipeline that selects a small set of quantum-feasible reactor-scale fault tree subtrees and establishes classical baselines for those candidates using SCRAM. The starting point is a reactor-scale subtree working set containing 30,885 subtrees extracted from a Phase 2B operational model. Gate 1 applies structural criteria, qubit upper bound criteria, and circuit depth proxy criteria consistent with near term quantum resource constraints, selecting 776 subtrees (2.513% of the working set). Gate 2 converts each Gate 1 candidate into an OpenPSA Model Exchange Format (MEF) representation, validates the MEF with SCRAM 0.16.2, and computes prime implicants for the top event. In the frozen Gate 2 run, all 776 candidates validate successfully and all 776 runs complete successfully. Across the 776 candidates, SCRAM returns between 3 and 5 prime implicants per subtree (median 3 for n = 5 and n = 6 basic events; median 4 for n = 8). Order-2 implicants constitute 85.83% of all 2,859 prime implicants identified. The order distribution exhibits a clear structural regularity: n = 6 subtrees yield exclusively order-2 implicants, while n = 5 and n = 8 subtrees exhibit mixed-order patterns attributable to their distinct gate topologies. SCRAM execution times are tightly clustered, with a run time median of 143.1 ms and a 95th-percentile of 176.1 ms across all 776 candidates. A depth proxy cross-validation against offline FakeTorino transpilation confirms that the Gate 1 depth criterion operates conservatively: the proxy value of 22 uniformly underestimates realized depth (39 excluding measurement gates, a 17-gate underestimate; 40 including measurement gates, an 18-gate underestimate), but all realized depths remain well within the 50-gate threshold. The resulting artifact bundle provides a defensible, fully reproducible classical baseline for subsequent hybrid and quantum evaluation.
This paper presents a standalone, audit-ready pipeline that selects a small set of quantum-feasible reactor-scale fault tree subtrees and establishes classical baselines for those candidates using SCRAM. The starting point is a reactor-scale subtree working set containing 30,885 subtrees extracted from a Phase 2B operational model. Gate 1 applies structural criteria, qubit upper bound criteria, and circuit depth proxy criteria consistent with near term quantum resource constraints, selecting 776 subtrees (2.513% of the working set). Gate 2 converts each Gate 1 candidate into an OpenPSA Model Exchange Format (MEF) representation, validates the MEF with SCRAM 0.16.2, and computes prime implicants for the top event. In the frozen Gate 2 run, all 776 candidates validate successfully and all 776 runs complete successfully. Across the 776 candidates, SCRAM returns between 3 and 5 prime implicants per subtree (median 3 for n = 5 and n = 6 basic events; median 4 for n = 8). Order-2 implicants constitute 85.83% of all 2,859 prime implicants identified. The order distribution exhibits a clear structural regularity: n = 6 subtrees yield exclusively order-2 implicants, while n = 5 and n = 8 subtrees exhibit mixed-order patterns attributable to their distinct gate topologies. SCRAM execution times are tightly clustered, with a run time median of 143.1 ms and a 95th-percentile of 176.1 ms across all 776 candidates. A depth proxy cross-validation against offline FakeTorino transpilation confirms that the Gate 1 depth criterion operates conservatively: the proxy value of 22 uniformly underestimates realized depth (39 excluding measurement gates, a 17-gate underestimate; 40 including measurement gates, an 18-gate underestimate), but all realized depths remain well within the 50-gate threshold. The resulting artifact bundle provides a defensible, fully reproducible classical baseline for subsequent hybrid and quantum evaluation.
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 work evaluates Constraint-Level QUBO (CL-QUBO) circuit execution on IBM Quantum hardware for 34 reactor-scale fault tree subtrees spanning 5–8 basic events, selected from the 776-member quantum-feasible candidate pool established in Paper 9 (Peters, 2026). Circuits were constructed using the CL-QUBO encoding and QAOA Alternating Operator Ansatz at depth p = 1, transpiled to both ibm_torino (133 qubits) and ibm_marrakesh (156 qubits), and executed under three IBM Runtime Sampler configurations (RL0, RL1, RL2) with identical bound parameters (β = 0.2, γ = 0.2) across all resilience levels. A total of six hardware jobs consumed 476 seconds (7.93 minutes) of quantum runtime across 8,192 shots per circuit. The results demonstrate that at this circuit scale, 10–16 logical qubits transpiling to 78–150 two-qubit gates at depths of 165–338, hardware output distributions are overwhelmingly noise-dominated by standard distributional metrics. Neither RL1 nor RL2 produces improvement; RL1 actively degrades output quality relative to RL0 on both backends. However, direct comparison of hardware top-probability outcomes against SCRAM-validated prime implicants from Paper 9 reveals substantial above-random minimal cut set (MCS) enrichment relative to the uniform-random baseline in the n = 8 groups (6.2× and 3.8× expected random rate in the top-200 outcomes), demonstrating that CL-QUBO circuits produce detectable MCS-correlated structure even in distributions that appear noise-dominated by aggregate metrics. These findings characterize the current observed performance ceiling for this CL-QUBO configuration on the tested IBM backends and provide both distributional and MCS-correctness baselines against which future hardware improvements can be measured.
This study presents a bounded, auditable quantum execution framework for probabilistic risk assessment (PRA) using OpenPRA-derived fault tree encodings and provides the first platform-integrated empirical characterization of structural scaling limits within the OpenPRA quantum execution workflow. A tri-provider architecture integrating local structural validation, IBM gate-based quantum hardware, and a D-Wave-ready interface is applied to 132 constraint-level QUBO (CL-QUBO) export artifacts retained from the OpenPRA quantum-feasible candidate pool. A systematic scaling gap analysis reveals that all 132 cases occupy exactly two qubit levels—5 qubits (23 cases, 17.4%) and 8 qubits (109 cases, 82.6%)—with zero semantically valid same-root expansions beyond 8 qubits. IBM Quantum hardware validation on ibm_marrakesh confirms bounded MCS recovery at both qubit levels, including exact hardware recovery (3/3 reference MCS) at 5 qubits and partial recovery (3/4 reference MCS) at 8 qubits, with job-level provenance for every execution. A hybrid filtering framework generates 4,692 synthetic cross-root expansion candidates, of which zero preserve semantic PRA validity; 14 selected 16-qubit candidates are validated through a deterministic structural execution validator, and three are executed on IBM hardware as stress tests (156 physical qubits after transpilation, 205–220 unique bitstrings observed per job). These results establish strong evidence that the observed 8-qubit ceiling is a property of the current CL-QUBO export pipeline applied to real reactor-scale fault trees, that scaling beyond this ceiling requires structural decomposition or alternative execution paradigms, and that the integrated OpenPRA quantum platform can execute, validate, and bundle evidence across the full pipeline with auditable provenance. No claim of quantum advantage or production PRA quantification is made.
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.
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.
This paper presents a migration case study: moving quantum-identified minimal cut set (MCS) recovery processing from ad hoc research scripts into a structured package within the OpenPRA monorepo, and validating the migration on an executed-only cohort of three reactor-scale fault tree subtrees from a Generic Pressurized Water Reactor model. Two of the three validated cases (0698, 1037) share the same structural subtree (root gate G:G348, topology Class A, 5 basic events) and achieved tier 1 exact hardware recovery (3/3 reference MCS each). The third case (0905, topology Class C, 8 basic events) achieved union sensitivity recovery (tier 1: 3/4, union: 4/4) with operator attention required. The package-based workflow achieved semantic parity with the accepted legacy script-era artifacts on all three cases, preserving recovery outcomes and recommendations while producing a cleaner package-native output format. The paper defines and defends semantic parity as the appropriate migration criterion for this workflow, establishes a traceable artifact acceptance chain, and demonstrates that executed-only filtering is necessary for a defensible validation cohort in this mixed-evidence batch to prevent conflating validated recovery evidence with unevidenced diagnostic candidates. Because the cohort comprises only two unique structural configurations, the findings are limited to migration correctness on a narrow validated set rather than broad workflow robustness. This paper does not claim quantum advantage or deployment readiness.