Fault tree analysis (FTA) is widely used for probabilistic risk assessment in complex engineered systems. When basic-event failure probabilities are uncertain, estimating system-level risk typically requires nested sampling procedures whose computational cost increases as higher precision is required. The propagation of these uncertainties through large-scale logical models creates a computational bottleneck, as classical computational simulations struggle to efficiently resolve risk metrics in high-dimensional parameter spaces. Advances in quantum computing have motivated the investigation of alternative computational approaches to probabilistic estimation problems. This work examines how concepts from quantum computing can be applied to the evaluation of fault trees and importance measures under parametric uncertainty. One approach involves discretizing uncertain basic-event failure probabilities and encoding them into quantum states in superposition, allowing multiple parameter realizations to be represented simultaneously within a single quantum circuit. Controlled rotations map these realizations to failure probabilities, and reversible logic implements the fault tree structure. Iterative Amplitude Estimation (IAE) is used to estimate the expected top-event probability with a potential for quadratic speedup over classical sampling. The same framework is applied to compute component importance measures, including Fussell–Vesely indices, by modifying the circuit to enforce perfect reliability of basic events. A case study of a small fault tree is presented to demonstrate the implementation and resulting system risk and importance values under uncertainty. Practical limitations related to circuit depth, gate decomposition, and current simulation constraints are identified and discussed.