Advances in data collection using inexpensive sensors have enabled monitoring the performance of dynamic systems, and to implement appropriate control actions to improve their performance. Moreover, engineering systems often operate under uncertain conditions; therefore, the real-time decision-making framework should not only consider real-time sensor data processing but also several uncertainty sources that may impact the performance of dynamic systems. In this paper, we investigate the modeling of such time-dependent system behavior using a dynamic quantum Bayesian network (DQBN), which is the quantum version of a classical dynamic Bayesian network (DBN). The DBN framework has been extensively used in various domains for its ability to model stochastic relationships between random variables across time. The use of the quantum amplitude amplification algorithm provides quadratic speedup for inference and prediction in Bayesian networks. In this paper, we combine the modeling capabilities of DBN with the computational advantage of quantum amplitude amplification for efficient modeling and control of time-dependent systems. We implement the proposed DQBN framework on IBM Q hardware, and compare its performance with classical DBN implementation and the IBM Qiskit simulator.
Advances in data collection using inexpensive sensors have enabled monitoring the performance of dynamic systems, and to implement appropriate control actions to improve their performance. Moreover, engineering systems often operate under uncertain conditions; therefore, the real-time decision-making framework should not only consider real-time sensor data processing but also several uncertainty sources that may impact the performance of dynamic systems. In this paper, we investigate the modeling of such time-dependent system behavior using a dynamic quantum Bayesian network (DQBN), which is the quantum version of a classical dynamic Bayesian network (DBN). The DBN framework has been extensively used in various domains for its ability to model stochastic relationships between random variables across time. The use of the quantum amplitude amplification algorithm provides quadratic speedup for inference and prediction in Bayesian networks. In this paper, we combine the modeling capabilities of DBN with the computational advantage of quantum amplitude amplification for efficient modeling and control of time-dependent systems. We implement the proposed DQBN framework on IBM Q hardware, and compare its performance with classical DBN implementation and the IBM Qiskit simulator.
Bayesian Networks (BN) are probabilistic graphical models that are widely used for uncertainty modeling, stochastic prediction and probabilistic inference. A Quantum Bayesian Network (QBN) is a quantum version of the Bayesian network that utilizes the principles of quantum mechanical systems to improve the computational performance of various analyses. In this paper, we experimentally evaluate the performance of QBN on various IBM QX hardware against Qiskit simulator and classical analysis. We consider a 4-node BN for stock prediction for our experimental evaluation. We construct a quantum circuit to represent the 4-node BN using Qiskit, and run the circuit on nine IBM quantum devices: Yorktown, Vigo, Ourense, Essex, Burlington, London, Rome, Athens and Melbourne. We will also compare the performance of each device across the four levels of optimization performed by the IBM Transpiler when mapping a given quantum circuit to a given device. We use the root mean square percentage error as the metric for performance comparison of various hardware.
Quantum Bayesian Networks (QBNs) offer a powerful framework for modeling uncertainty and decision-making in complex systems. This paper explores the implementation of a novel QBN architecture that dynamically adjusts connectivity based on observed evidence, enhancing inference and decision-making capabilities. We introduce a dynamic connectivity mechanism that iteratively refines the network topology to better represent the underlying uncertainty. The resulting QBN exhibits improved performance in scenarios requiring adaptive decision-making compared to static network configurations. This work contributes to the advancement of Bayesian network inference and highlights the potential for more robust and flexible models.
Abstract In multi-agent systems, Bayesian networks are pivotal for inference and decision-making under uncertainty, yet they face significant challenges, such as high computational complexity and slow decision speed. Quantum computing, leveraging superposition and entanglement, offers potential advantages for solving certain complex problems. Therefore, exploring Bayesian networks within the quantum multi-agent framework promises enhanced inference and decision-making capabilities. While quantum Bayesian networks for inference have been extensively studied, quantum dynamic Bayesian networks for inference and quantum decision networks for decision-making remain underexplored. In the noisy intermediate-scale quantum (NISQ) era, quantum computers struggle to process the long-term temporal structures of dynamic Bayesian networks due to limited resources. To address this, we propose a recursive quantum-classical hybrid Bayesian network inference method, which decomposes dynamic Bayesian networks into smaller subnetworks along the time series. Each subnetwork is represented by a reduced-scale quantum circuit, and the forward and backward operators are computed recursively, enabling efficient filtering and smoothing inference. In addition, we propose an optimal decision-making method based on quantum decision networks, which maps utility values to quantum probabilities and identifies the optimal action by determining the quantum state corresponding to the maximum expected probability. We validate the effectiveness of these algorithms using the IonQ quantum simulator and compare their performance with classical methods. The results demonstrate that our proposed quantum algorithms can effectively perform inference and decision-making tasks well on NISQ devices. The proposed methods provide a foundation for collaborative inference and decision-making within the quantum multi-agent framework.
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.
This thesis explores the intersection of Bayesian inference and quantum computing, with a particular focus on developing and analyzing quantum approaches to probabilistic modeling. The motivation arises from the limitations of classical inference methods, which often become intractable when applied to high-dimensional distributions and complex Bayesian networks. By leveraging quantum algorithms, the work investigates how probabilistic reasoning can benefit from computational speedups, scalability, and more efficient handling of uncertainty.The implementation targets canonical benchmark problems—the Sprinkler Network and the Asia Network—where both classical and quantum Bayesian inference techniques are applied and compared. Using Qiskit, the thesis demonstrates how quantum circuits can encode probabilistic models through parameterized rotations and controlled operations, and how posterior distributions can be computed by sampling and amplitude amplification. Comparative experiments systematically evaluate the accuracy, variance, and scalability of quantum Bayesian inference against classical baselines, highlighting trade-offs between precision and shot counts while exploring the potential for quadratic speedups.The results show that although present-day hardware constraints, such as limited qubit counts and noise, restrict large-scale deployment, quantum implementations already display strong promise for complex probabilistic reasoning tasks. Importantly, the conclusions underscore the role of quantum Bayesian networks as a pathway toward practical quantum-enhanced machine learning.
Quantum state tomography is a crucial technique for characterizing the state of a quantum system. However, traditional tomography methods often suffer from high measurement complexity and require a large number of measurements to achieve high accuracy. This paper proposes a novel approach utilizing Dynamic Bayesian Networks (DBNs) to iteratively refine quantum state tomography measurements. The DBN learns the relationship between the quantum state estimate and the expected measurement outcomes, allowing it to intelligently guide the measurement process. This approach significantly reduces the number of measurements needed while simultaneously improving the accuracy of the state reconstruction. We present a theoretical framework for the DBN-based tomography and demonstrate its potential through a mathematical analysis of the iterative estimation process. The core claim of this work is that DBNs offer a more efficient and accurate method for quantum state tomography compared to conventional techniques.