Quantum Bayesian Networks construction, prediction, and inference

Abstract

Thesis (Ph.D.)-- Wichita State University, College of Engineering, Dept. of of Industrial, Systems and Manufacturing EngineeringIn recent years, quantum computing has garnered increasing attention for its potential to outperform classical methods in computational efficiency. While demonstrations of quantum supremacy remain rare, algorithms leveraging amplitude amplification have exhibited notable advantages over classical approaches, particularly for NP-hard problems found in optimization, uncertainty modeling, and machine learning. This research explores the application of quantum computing to Bayesian Networks (BNs), widely used for modeling stochastic systems in probabilistic prediction, risk analysis, and system health monitoring—tasks that become computationally intensive at scale. We propose a method called C-QBN for designing quantum circuits that represent generic discrete BNs, with potential applicability to continuous variables via discretization. Efficient quantum representation of Bayesian Networks can facilitate the application of other quantum algorithms, for performing inference or prediction, for instance. To reduce quantum resource demands, we introduce AD-QBN, an improved version of C-QBN that minimizes multi-qubit gate usage, leading to simpler, more hardware-efficient circuits. Building upon this, we extend the approach to Dynamic Quantum Bayesian Networks (DQBNs), capable of modeling time-dependent systems by capturing relationships across and within time steps. We validate these frameworks—C-QBN, AD-QBN, and DQBN—through multiple case studies, including stock prediction, risk assessment, and real-time health monitoring under uncertainty. Additionally, we examine the use of variational quantum circuits to approximate QBNs on Noisy Intermediate-Scale Quantum (NISQ) devices, offering a practical path forward while scalable quantum hardware remains in development. All implementations are conducted in Python using IBM’s Qiskit simulator and are benchmarked against classical BN models