Quantum Fault Trees and Minimal Cut Sets Identification

Abstract

Fault Trees represent an essential tool in the reliability and risk assessment of complex engineering systems. One of the core tasks in Fault Tree analysis is the identification of Minimal Cut Sets, defined as groups of components that present the least path of resistance toward a system's failure. Nonetheless, minimal cut set identification remains a highly challenging problem due to the exponential growth in feasible configurations as the system size increases linearly. Recently, quantum computation has been heralded as a promising tool to tackle computational challenges of increased complexity. However, its integration into reliability engineering, and in particular to challenges related to Fault Tree modeling, is still underexplored. To fill this relevant gap, this paper integrates quantum computation into the Fault Tree Model to assess its capabilities for minimal cut set identification. To this end, this paper proposes a novel approach to encode a fault tree into a quantum algorithm and perform the identification of minimal cut sets via the application of the Grover operator. For validation purposes, a series of theoretical and numerical results, the latter obtained using a quantum simulator, are presented in which the proposed algorithm is compared against a state-of-the-art non-quantum approach.