This paper explores the potential application of quantum and hybrid quantum–classical neural networks in power flow analysis. Experiments are conducted using two datasets based on 4-bus and 33-bus test systems. A systematic performance comparison is also conducted among quantum, hybrid quantum–classical, and classical neural networks. The comparison is based on (i) generalization ability, (ii) robustness, (iii) training dataset size needed, (iv) training error, and (v) training process stability. The results show that the developed hybrid quantum–classical neural network outperforms both quantum and classical neural networks, and hence can improve deep learning-based power flow analysis in the noisy-intermediate-scale quantum (NISQ) and fault-tolerant quantum (FTQ) era.
In this paper, we develop a hybrid quantum physics-informed neural network (QPINN) for power flow analysis (PF). Two important modifications contribute to the enhanced performance of QPINN: (i) a parameterized quantum circuit is integrated within the neural network architecture, and (ii) a physical loss function is developed based on the PF equations. Experiments are conducted using a small-size dataset based on a 4-bus test system. A linear regression model (LR) and a multilayer perceptron (MLP) are used to perform a systematic performance comparison. The comparison is based on the (i) training error, (ii) validation error, (iii) generalization ability, and (iv) robustness. The results show that QPINN outperforms both LR and MLP and, therefore, can improve deep learning-based PF analysis in the noisy-intermediate-scale quantum (NISQ) era.
This study presents a systematic comparison between hybrid quantum-classical neural networks and purely classical models across three benchmark datasets (MNIST, CIFAR100, and STL10) to evaluate their performance, efficiency, and robustness. The hybrid models integrate parameterized quantum circuits with classical deep learning architectures, while the classical counterparts use conventional convolutional neural networks (CNNs). Experiments were conducted over 50 training epochs for each dataset, with evaluations on validation accuracy, test accuracy, training time, computational resource usage, and adversarial robustness (tested with
ε=0.1 perturbations).Key findings demonstrate that hybrid models consistently outperform classical models in final accuracy, achieving {99.38\% (MNIST), 41.69\% (CIFAR100), and 74.05\% (STL10) validation accuracy, compared to classical benchmarks of 98.21\%, 32.25\%, and 63.76\%, respectively. Notably, the hybrid advantage scales with dataset complexity, showing the most significant gains on CIFAR100 (+9.44\%) and STL10 (+10.29\%). Hybrid models also train 5--12
× faster (e.g., 21.23s vs. 108.44s per epoch on MNIST) and use 6--32\% fewer parameters} while maintaining superior generalization to unseen test data.Adversarial robustness tests reveal that hybrid models are significantly more resilient on simpler datasets (e.g., 45.27\% robust accuracy on MNIST vs. 10.80\% for classical) but show comparable fragility on complex datasets like CIFAR100 ($\sim$1\% robustness for both). Resource efficiency analyses indicate that hybrid models consume less memory (4--5GB vs. 5--6GB for classical) and lower CPU utilization (9.5\% vs. 23.2\% on average).These results suggest that hybrid quantum-classical architectures offer compelling advantages in accuracy, training efficiency, and parameter scalability, particularly for complex vision tasks.
Abstract Quantum Machine Learning (QML) is an emerging field at the intersection of quantum computing and machine learning that aims to enhance classical learning methods by leveraging principles such as superposition and entanglement. However, skepticism remains regarding its practical advantages, particularly due to the limitations of noisy intermediate-scale quantum (NISQ) devices. This study addresses these concerns through a systematic evaluation of Quantum Neural Networks (QNNs), quantum-inspired counterparts of Artificial Neural Networks (ANNs). We construct and analyze 12 distinct QNN configurations by combining two quantum feature maps with six entanglement strategies for ansatz design. Experiments conducted on a wind energy dataset show that QNNs can achieve competitive or superior performance compared to classical baseline models, with the best-performing configuration (QNN-3) reaching an R 2 score of up to 0.94 when forecasting wind power output using four input features. In addition, we provide a detailed analysis of simulation time across different configurations, highlighting trade-offs between model complexity and computational cost. These findings demonstrate the potential of QNNs as viable models for predictive tasks and contribute to the ongoing evaluation of QML in real-world applications.
Given the recent prominence of Noisy Intermediate Scale Quantum (NISQ) devices, hybrid quantum-classical neural networks have recently drawn a lot of excitement as a potential solution to improving learning efficiency. Our current paper describes a Hybrid Quantum-Classical Convolutional Neural Network (HQCNN) which is defined as a pretrained backbone of ResNet-18 and a small quantum-enhanced feature-transformation layer of Qiskit. The convolutional high-dimensional features are reduced to the classical eight-dimensional one, which in turn is encoded into a four-qubit parameterized quantum circuit. The resultant quantum expectation values are combined with the compressed features to come up with a hybridized representation of twelve dimensions, used to classify multi-class dataset. Experimental analysis of CIFAR10 data has shown that the suggested HQCNN achieves a test accuracy of 94.74% and improves class-wise precision, recall, and F1-scores than a number of existing hybrid models while using a significantly smaller number of latent features. More investigation into the quantum module indicates that it is predictable about scalability to batch, resistant to perturbations in features, and efficiently performed by evaluating circuit vectors. These results indicate that compact and expressive representations of images that can be helpful in the NISQ era can be acquired using hybrid architectures, thus providing a practical way to forward the benefits of quantum to modern deep-learning pipelines.
The unprecedented success of classical neural networks and the recent advances in quantum computing have motivated the research community to explore the interplay between these two technologies, leading to the so-called quantum neural networks. In fact, universal quantum computers are anticipated to both speed up and improve the accuracy of neural networks. However, whether such quantum neural networks will result in a clear advantage on noisy intermediate-scale quantum (NISQ) devices is still not clear. In this paper, we propose a systematic methodology for designing quantum layer(s) in hybrid quantum–classical neural network (HQCNN) architectures. Following our proposed methodology, we develop different variants of hybrid neural networks and compare them with pure classical architectures of equivalent size. Finally, we empirically evaluate our proposed hybrid variants and show that the addition of quantum layers does provide a noticeable computational advantage.
Alternative Current Optimal Power Flow (AC-OPF) is essential for efficient power system planning and real-time operation but remains an NP-hard and non-convex optimization problem with significant computational challenges. This paper proposes a novel hybrid classical-quantum deep learning framework for AC-OPF problem, integrating parameterized quantum circuits (PQCs) for feature extraction with classical deep learning for data encoding and decoding. The proposed framework integrates two types of residual connection structures to mitigate the ``barren plateau" problem in quantum circuits, enhancing training stability and convergence. Furthermore, a physics-informed neural network (PINN) module is incorporated to guarantee tolerable constraint violation, improving the physical consistency and reliability of AC-OPF solutions. Experimental evaluations on multiple IEEE test systems demonstrate that the proposed approach achieves superior accuracy, generalization, and robustness to quantum noise while requiring minimal quantum resources.