Semantic-Preserving QUBO Encodings for Fault Tree Analysis: Hierarchical Repair and Constraint-Level Formulations

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.