Quantum Fault Trees and Minimal Cut Sets Identification

Abstract

Fault Trees represent an essential tool in the reliability and risk assessment of engineering systems. By decomposing the structure of the system into Boolean function, Fault Trees allow the quantitative and qualitative analysis of the system. One of the main important 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. Identifying them allows reliability engineers to enhance the reliability and safety of the system, making system failures less likely to occur. However, the minimal cut set identification problem is challenging to solve, due to the exponential growth experienced in the number of feasible configurations as the system's size grows linearly. Over the last few years, quantum computation has been heralded as a promising tool to tackle computational challenges of increased complexity. The reason for this is the promising prospects that the use of quantum effects has for challenging computational tasks. However, its application into Probabilistic Risk Assessment and reliability engineering, and in particular to challenges related to the Fault Tree model, is still uncharted territory. To fill this gap, the objective of the paper is to integrate quantum computation into the Fault Tree Model and present an assessment of their capabilities for the minimal cut set identification problem. To this end, this paper proposes a novel algorithm to encode a fault tree into a quantum computer and to perform the identification of minimal cut sets with increased efficiency via the application of the Quantum Amplitude Amplification protocol. 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 traditional approaches, such as Monte Carlo sampling.