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.
Devin Peters (Sat,) studied this question.