Incorporating Continuous Distributions in Quantum Bayesian Networks for Reliability Assessment

Operational demands in industries, such as the energy sector, underscore the critical need for reliable equipment capable of withstanding long-term planning and unpredictable factors. Reliability assessment is important for maintaining productivity and optimizing maintenance strategies, especially in scenarios where data limitations challenge traditional assessment methods. In this context, Bayesian inference has emerged as a dynamic tool to update reliability estimates using data from various hierarchical levels. However, conventional simulation techniques may lack computational efficiency when dealing with the reliability estimation of complex systems, creating opportunities to explore alternative approaches such as quantum computation techniques. Quantum Computing leverages principles of quantum mechanics, such as superposition and entanglement, to try to address these computational challenges more effectively. Previous works have applied quantum Bayesian networks using amplitude amplification methods to the context of risk and reliability, focusing on nodes representing discrete probability distributions. This research aims to enhance this approach by incorporating continuous marginal and conditional probabilities into the analysis, which is particularly relevant for systems that rely on these distributions to model events. We explore the encoding of continuous probability distributions within the amplitude amplification framework, aiming to improve the efficiency and precision of probabilistic inference. Additionally, we apply this methodology to Bayesian networks, benchmarking the performance of quantum methods against classical simulation techniques like Monte Carlo to identify scenarios where quantum techniques demonstrate clear advantages.

Keywords: Reliability assessment, Quantum computing, Bayesian networks.