Quantum Annealing Approaches for Minimal Cut Set Identification in Fault Trees

The identification of Minimal Cut Sets (MCS) in Fault Trees (FT) is central to Probabilistic Safety Assessment (PSA) but remains computationally challenging. While gate-based quantum algorithms have been explored, Quantum Annealing (QA) has not yet been applied to this industrial use case. This work investigates the application of QA to MCS identification by modeling the FT as a boolean function and implementing three existing SAT to Quadratic Unconstrained Binary Optimization (QUBO) encoding strategies. We evaluate these encodings using generated 3-SAT instances as well as realistic FT benchmarks, and conduct experiments on a simulated annealer and two D-Wave architectures. Our results show that the encoding with reusable auxiliary variables is the most efficient in terms of qubit requirements and embedding scalability. In addition, the Zephyr architecture provides improved embeddability compared to Pegasus, reflected in reduced chain break occurrences and better performance on larger instances. Across these experiments, QA demonstrates the ability to sample diverse valid solutions, making it suitable for exploring the solution space of MCS problems. However, its performance remains limited by hardware constraints and the maximum number of possible shots, which prevent exhaustive identification of all solutions in larger instances.