Quantum Bayesian Decision-Making

Ece Çiǧdem Mutlu, Özlem Özmen Garibay

Hao Jie Shi, Ming Zhang, Haoqiang Chen +2 more

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.

Hervé Zwirn C

Hao Jie Shi, Chenghao 成豪 Han 韩, Peng 鹏 Wang 王 +1 more

Abstract Although quantum Bayesian networks provide a promising paradigm for multi-agent decision-making, their practical application faces two challenges in the noisy intermediate-scale quantum (NISQ) era. Limited qubit resources restrict direct application to large-scale inference tasks. Additionally, no quantum methods are currently available for multi-agent collaborative decision-making. To address these, we propose a hybrid quantum–classical multi-agent decision-making framework based on hierarchical Bayesian networks, comprising two novel methods. The first one is a hybrid quantum–classical inference method based on hierarchical Bayesian networks. It decomposes large-scale hierarchical Bayesian networks into modular subnetworks. The inference for each subnetwork can be performed on NISQ devices, and the intermediate results are converted into classical messages for cross-layer transmission. The second one is a multi-agent decision-making method using the variational quantum eigensolver (VQE) in the influence diagram. This method models the collaborative decision-making with the influence diagram and encodes the expected utility of diverse actions into a Hamiltonian and subsequently determines the intra-group optimal action efficiently. Experimental validation on the IonQ quantum simulator demonstrates that the hierarchical method outperforms the non-hierarchical method at the functional inference level, and the VQE method can obtain the optimal strategy exactly at the collaborative decision-making level. Our research not only extends the application of quantum computing to multi-agent decision-making but also provides a practical solution for the NISQ era.

Jincheng Zhang

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.