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.
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.
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.
Abstract The emergence of noisy intermediate-scale quantum (NISQ) devices has fueled the development of hybrid quantum-classical algorithms for machine learning (ML), promising potential advantages over classical methods. However, the practical efficacy of these algorithms remains uncertain due to challenges like noise susceptibility, trainability issues, and a lack of rigorous benchmarking. This study presents a comprehensive empirical evaluation of two flagship hybrid algorithms the Variational Quantum Eigensolver (VQE) for classification and the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization against state-of-the-art classical baselines under equivalent resource constraints. Through extensive simulations incorporating realistic noise models, we demonstrate that while these quantum approaches achieve competitive performance (e.g., 91.2% accuracy for VQE on a binary classification task), they consistently underperformed optimized classical models like Support Vector Machines (94.8% accuracy) and require orders of magnitude more computational time. Furthermore, we provide empirical validation of critical barriers to scalability, including the barren plateau phenomenon and significant performance degradation under noise, even with advanced error mitigation. Our results indicate that for the tasks studied, current NISQ era algorithms do not yet provide a tangible quantum advantage. This work contributes a rigorous benchmarking framework and a critical, realistic assessment of the field, suggesting that future progress hinges on fundamental algorithmic innovations and hardware improvements rather than incremental refinements of existing paradigms.
The astounding acceleration in Artificial Intelligence and Quantum Computing advances naturally gives rise to a line of research, which unrolls the potential advantages of quantum computing on classical Machine Learning tasks, known as Quantum Machine Learning or Quantum Machine Intelligence. The typical objectives are either (1) exploring the potential quantum advantages on classical learning tasks or (2) levering well-established classical ML algorithms to tackle quantum-related problems on Noisy Intermediate-Scale Quantum (NISQ) devices. Along the second research direction, we study Quantum Neural Networks (QNNs) to accomplish the purpose of Bayesian learning. By observing a wide range of studies on QNNs, in which the sole training method is based on frequentist training, we find that Bayesian learning benefits QNNs from two aspects. First, Bayesian-trained models enjoy a high level of generalization due to the prior and posterior distribution usage compared to frequentist training, which will be justified by this paper’s theoretical study of model capacity. Second, Bayesian Inference offers epistemic uncertainty estimation, which merits the decision-making process. It is worth mentioning that frequentist-trained QNNs generally lack this desirable property. Under the Bayesian training procedure, our derived models can be considered a new class of QNNs (called BayesianQNNs) which possesses both desirable properties of Bayesian Inference while maintaining comparable predictive performance as frequentist counterparts. The proposed Bayesian Quantum Neural Networks is justified by empirical evidence from numerical experiments.
Background: This paper investigates hybrid quantum–classical optimization approaches for addressing core supply chain management (SCM) problems. A unified hybrid framework is implemented and evaluated across five representative domains: vehicle routing, scheduling, facility location, inventory optimization, and demand forecasting. Methods: The framework integrates quantum algorithms—namely the Quantum Approximate Optimization Algorithm (QAOA), Quantum Annealing (QA), and the Variational Quantum Eigensolver (VQE)—with classical constraint-handling and local refinement procedures in an iterative workflow. Quantum solvers are employed for global solution exploration, while classical optimization ensures feasibility and convergence stability. Results: Experiments conducted on standardized synthetic benchmarks demonstrate that the proposed hybrid framework consistently outperforms classical-only and quantum-only baselines, achieving 12–18% reductions in operational costs and 20–35% faster convergence. In routing and fulfilment tasks, quantum-generated candidate solutions provide effective warm starts for classical refinement. Robustness analysis based on stochastic SCM simulations further indicates lower performance variance under uncertainty. Conclusions: These results demonstrate that hybrid quantum–classical optimization constitutes a practical and scalable strategy for near-term SCM decision-making under current Noisy Intermediate-Scale Quantum (NISQ) hardware constraints.
The hardware noise and drift, combined with the fragility of stationary hybrid algorithms like the variational quantum eigensolver (VQE), limit the usefulness of noise quantum advantage accessed through Noisy intermediate-scale quantum (NISQ) processors, but allow near-term quantum advantage. In this paper, a Hybrid Quantum-Classical Adaptive Intelligence Framework is suggested, which bridges the gap between quantum hardware, a parameterized quantum circuit, explicit error-mitigation routines, and a controller trained through learning. The quantum subsystem prepares variational states and calculates the expectation values of the problem Hamiltonian, and an AI/ML model approximates an online noise probability signal and moves an optimizer based on reinforcement learning (RL). The RL policy chooses the parameter updates and enables mitigation measures depending on noise-sensitive state functions, such as energy, gradient norm, and estimated noise level. It was demonstrated experimentally using a simulated NISQ-style molecular Hamiltonian that the adaptive controller can reduce the error in the absolute ground state of the system by about 52.8 percent versus a standard static VQE baseline using the same ansatz. The integrated classifier that drives the process of mitigation is accurate with 97 percent accuracy, 100 percent precision, 92 percent recall, 95.9 F1-score, and 99.5 AUC, which shows reliable decision-making with minimal false alarms. All these findings indicate that the close-knit quantum-classical adaptivity can significantly contribute to the robustness and accuracy of VQE-like workloads on NISQ and serve as a scalable template to design noise-aware hybrid algorithms in the future.
This paper explores the synergistic combination of Bayesian inference and quantum computing for optimizing probabilistic graph models. Traditional Bayesian inference, particularly with complex graph structures, faces significant computational challenges. Quantum computing, leveraging its inherent parallelism, offers a promising avenue for accelerating these inference processes. We propose a framework that translates probabilistic graph models into quantum circuits, employing variational quantum algorithms such as Variational Quantum Eigensolver (VQE) or Quantum Approximate Optimization Algorithm (QAOA) to optimize the model parameters and expedite the inference. This approach aims to enhance both the accuracy and efficiency of Bayesian inference, addressing a critical bottleneck in various applications, including machine learning, statistical inference, and decision-making under uncertainty. The core claim of this research is the effective integration of Bayesian inference and quantum computing to accelerate the inference process. The underlying mechanism involves the transformation of probabilistic graph models into quantum circuits and utilizing quantum algorithms for optimization. This work represents a novel approach to tackling computationally intensive Bayesian inference problems, paving the way for more sophisticated and efficient probabilistic modeling. ---