Abstract We demonstrate that any Euclidean-time quantum mechanical theory may be represented as a neural network, ensured by the Kosambi-Karhunen-Loeve theorem, mean-square path continuity, and finite two-point functions. The additional constraint of reflection positivity, which is related to unitarity, may be achieved by a number of mechanisms, such as imposing neural network parameter space splitting or the Markov property. Non-differentiability of the networks is related to the appearance of non-trivial commutators. Neural networks acting on Markov processes are no longer Markov, but still reflection positive, which facilitates the definition of deep neural network quantum systems. We illustrate these principles in several examples using numerical implementations, recovering classic quantum mechanical results such as Heisenberg uncertainty, non-trivial commutators, and the spectrum.

Detecting quantum hacking attacks for continuous-variable quantum key distribution using quantum neural network

Stochastic quantum neural networks for neuroinspired intelligence: Mathematical foundations, comparative benchmarks, and prospects

Bit flip attack-guided mixed-precision neural network quantization

The rising environmental cost of deep learning has placed Green AI, which promotes focus on reducing the carbon footprint of AI, at the forefront of sustainable computing. In this study, we investigate Quantum Machine Learning (QML) as a novel and energy-efficient alternative by benchmarking two quantum models, the Quantum Neural Network (QNN) and Quantum Long Short-Term Memory (QLSTM), on the N-BaIoT anomaly detection dataset. Our first phase of experiments compares the QNN and QLSTM models using ten distinct quantum circuit designs (ansätze A1–A10). We systematically compare trade-offs between classification performance, model complexity, training time, and energy consumption. The results indicate that simpler QNN ansätze can achieve accuracy comparable to more complex ones while consuming significantly less energy and converging faster. In particular, QNN with ansatz A4 provided the optimal balance between performance and energy efficiency, consistently outperforming QLSTM across most metrics. A detailed energy breakdown confirmed GPU usage as the dominant source of power consumption, underscoring the importance of circuit-efficient quantum design. To contextualize QML’s viability, we conducted a second phase of experiments comparing quantum models with three benchmark classical machine learning models: Artificial Neural Network (ANN), Long Short-Term Memory (LSTM), and CatBoost. We find that the classical models demonstrated faster training times and lower energy consumption, highlighting and contrasting the maturity of algorithmic development that classical ML algorithms have already seen. Finally, we examined the energy implications of developing quantum models on actual quantum hardware. This third phase of experiments compared training on IBM Qiskit’s emulation environment (running on GPU servers) versus execution on real IBM Quantum hardware. Highlighting the significant differences in execution time and energy footprint, extrapolated results indicate that quantum hardware still incurs higher energy costs. This suggests that further hardware-aware ansätz optimization and improvements in quantum infrastructure are essential to realizing carbon-efficient QML at scale.

Quantum computing (QC) represents a revolutionary paradigm in information processing, leveraging quantum mechanical phenomena (superposition, entanglement, quantum interference, and quantum tunneling) to perform calculations in fundamentally different ways than classical computing (CC). While CC processes information sequentially through Boolean logic operations on discrete binary states (0 s and 1 s), quantum computers manipulate qubits that can exist in superpositions of states, enabling parallel operations on exponentially large state spaces. Despite claims regarding "quantum supremacy," QC remains in its early developmental stages, comparable to the CC of the 1950s and 1960s. True quantum supremacy, where quantum computers demonstrate definitive, practical advantages over classical computers for well-defined tasks, has not yet been established. Practical applications face real challenges, ie, decoherence, high error rates, and demanding error correction requirements. Three developmental phases are projected: noisy intermediate-scale quantum systems by 2030, broad quantum advantage from 2030 to 2040, and full-scale fault tolerance after 2040. Does QC offer solutions to fundamental problems that classical systems, including supercomputers and artificial intelligence, cannot already resolve? While conventional technologies continue to advance agricultural capabilities through machine learning (ML) and complex optimization, quantum approaches may potentially transform domains that require molecular-level simulations (such as soil chemistry and rumen microbial interactions) or exponentially complex optimization problems in resource allocation. Quantum ML models, such as quantum neural networks, generative adversarial networks, and autoencoders, are being explored in quantum-classical hybrids, which have shown potential for faster optimization and higher-dimensional data representation; but, these advantages remain largely conceptual. The value proposition of QC in agriculture ultimately depends on whether the field's most pressing challenges involve quantum mechanical processes that classical computers cannot simulate efficiently or optimization problems of such complexity that quantum algorithms would provide substantial practical advantages over classical approaches. The agricultural community must also address societal implications, such as access equity, data ownership, algorithmic transparency, and educational preparedness for this emerging technology.

ABSTRACT The proposed work developed a robust hybrid quantum neural network model (HQNN) to mitigate the model overfitting problem for MRI brain tumour diagnosis. As quantum computing is the future of computation, the proposed work analyzed the impact of quantum layers on HQNN architectures and quantum advantages in improving model generalisation through an ablation study. We designed a single-layered shallow 10-Qubit parameterised quantum circuit (PQC) to reduce the model’s overfitting. Fifteen HQNN models were designed, incorporating a diverse set of quantum gate arrangements to explore their effects on model performance. Through ablation experiments, the proposed work utilised the substantial impact of single-layered shallow PQC with RX rotation, H-Gate superposition, and CZ entanglement in improving model expressivity and more stable performance on validation data, and enhanced the model's robustness. The proposed PQC compensates for the reduced regularisation effect caused by turning off 10% of neuron activations at each training step in the HQNN model. It improved the validation accuracy of the model by 4.73%, indicating better generalisation than classical FCNN models. The proposed work used brain tumour classification datasets from Kaggle and figshare repositories. We compared our HQNN model with state-of-the-art (SOTA) methods on standard MRI brain tumour datasets. The proposed HQNN model outperformed the SOTA methods with 98.17% test accuracy in binary classification and 96.97% test accuracy in multi-class classification.

Abstract Clustering high-dimensional data with inherent geometric symmetries is a key challenge in unsupervised learning. While traditional algorithms like K-Means struggle with complex data structures, existing quantum methods often lack equivariance and face scalability issues on Noisy Intermediate-Scale Quantum (NISQ) hardware. This creates a need for a clustering approach that can effectively handle structured data. We introduce the p4m Equivariant Quantum Clustering (EQC) framework, a novel approach that integrates equivariant quantum neural networks with quantum kernel methods. Our model utilizes an 8-qubit quantum circuit with p4m symmetry-preserving operations to ensure robust feature extraction. We employ a hybrid quantum-classical optimization strategy to tune the model parameters. We evaluated the EQC framework on the MNIST and Quark-Gluon datasets. On the Quark-Gluon dataset, EQC achieved a Silhouette Score of 0.512 and 74.8% accuracy, a significant improvement over classical K-Means (Silhouette Score: 0.183; Accuracy: 58.4%). The model also demonstrated state-of-the-art performance on MNIST, achieving a Silhouette Score of 0.557 and 76.3% accuracy, consistently surpassing other quantum and classical baselines. The EQC framework sets a new benchmark for unsupervised learning on symmetric data. By successfully integrating equivariance into a quantum kernel method, our approach provides a scalable and highly accurate solution for near-term quantum applications and quantum-enhanced data analysis in complex, real-world scenarios.

With the advent of quantum computing, researchers have explored the applicability and any potential advantages of quantum algorithms. This study investigates the application of Quantum Machine Learning (QML) models for regression tasks. Utilizing two distinct CERN datasets (Dielectron events and Proton collision), we investigate prediction accuracy using two QML algorithms, namely Quantum Neural Network (QNN) and Quantum Long Short-Term Memory (QLSTM). We also discuss the comparative analysis and computational efficiency of QNN and QLSTM compared to classical regression methods. The results show that while the two QML models gave comparable accuracy scores to some of the classical models, the best scores were still achieved by some of the more advanced classical algorithms such as CatBoost. Further analysis of the QNN and QLSTM algorithms using multiple ansätz designs showed that increased circuit complexity did not yield substantial improvements in prediction accuracy. These findings suggest that QML models, especially QLSTM with simpler ansätz designs, offer a promising approach for modeling high-energy physics data, and highlight the importance of balancing circuit complexity with performance. The study also underscores the need for further evaluation of these algorithms on quantum hardware to better understand real-world applicability.

Abstract This study explores the evolution of polymer composites in naval and aerospace applications, specifically their use in high-stress components such as aircraft wings and fuselages. It highlights the impact of resonance on performance and safety, emphasizing the benefits of the vibratory wet lay-up technique over traditional methods. This innovative approach improves the fiber-resin interface, reduces voids, and enhances material properties through controlled vibration. Focusing on composite T-joint materials, the research assesses the effects of vibration on mechanical properties using polymer composites, PVC foam, glass fiber, and epoxy resin. These materials were fabricated using both standard and vibratory wet lay-up methods to optimize resin distribution and minimize voids. Mechanical properties were evaluated through tensile testing, three-point bending, Shore hardness tests, and water absorption experiments. Advanced machine learning techniques, such as Quantum Neural Networks (QNN) and the Puma Optimization Algorithm (POA), were employed for predictive analysis. The hybrid QNN-POA model proved to be the most accurate, achieving a mean error of just 0.16, surpassing traditional approaches. Experimental results revealed that TJ1 composites, particularly With Vibration Assistance (W-VA), exhibited the highest load-bearing capacity, reaching 9000 N with 8.36 mm displacement in tensile tests and 13,000 N with 11 mm displacement in bending tests. Although TJ2 and PVC composites also performed well, they exhibited slightly higher displacements. Overall, the study confirmed TJ1's superiority for high-load aerospace applications due to its enhanced strength and minimal displacement under vibration.

This study investigates hybrid quantum neural networks for fruit quality assessment, with a focus on the impact of the entangling gate choice. Two architectures were developed: NNQEv1, utilizing controlled-NOT (CNOT) gates, and NNQEv2, employing controlled-phase (CZ) gates. A theoretical justification is provided, based on gate decomposition and hardware-aware noise considerations, suggesting the CZ-based architecture is likely to be more stable. The performance of the models was evaluated through the computational execution of their quantum circuits on classical hardware and compared against classical and state-of-the-art deep learning models. The proposed models demonstrated competitive performance, achieving test accuracies of 98.7% on MNIST, 98.6% on the FruitQ dataset, and 96.7% on a custom, data-scarce Apple dataset. The experimental results align with the theoretical analysis: the CZ-based NNQEv2 model, when compared to the CNOT-based NNQEv1, consistently showed more stable training dynamics and yielded tighter confidence intervals in cross-validation. This work presents a foundational, computational study on the role of gate-level design choices, intended to inform the development of future quantum machine learning algorithms.

Quantum reservoir computing (QRC) offers a promising paradigm for harnessing quantum systems for machine learning tasks, especially in the era of noisy intermediate-scale quantum devices. While information-theoretical benchmarks like short-term memory capacity (STMC) are widely used to evaluate QRC performance, they fail to provide insights into the physical mechanisms underlying these quantum neural networks. We establish a quantitative connection between the optical absorption spectrum of a quantum reservoir and its memory performance, revealing that optimal STMC aligns directly with maximal absorption, providing a physical explanation for the previously reported "sweet-spot" behavior in QRC performance as a function of dissipation. This connection bridges quantum information theory with experimentally accessible physical properties, opening pathways for targeted engineering of quantum reservoir computers with optimized performance for specific tasks.

Background: Quantum Neural Networks (QNNs) combine quantum computing and artificial intelligence to provide powerful solutions for high-dimensional data analysis. In magnetic resonance imaging (MRI), they address the challenges of advanced imaging sequences and data complexity, enabling faster optimization, enhanced feature extraction, and real-time clinical applications. Methods: A literature review using Scopus, PubMed, IEEE Xplore, ACM Digital Library and arXiv identified 84 studies on QNNs in MRI. After filtering for peer-reviewed original research, 20 studies were analyzed. Key parameters such as datasets, architectures, hardware, tasks, and performance metrics were summarized to highlight trends and gaps. Results: The analysis identified datasets supporting tasks like tumor classification, segmentation, and disease prediction. Architectures included hybrid models (e.g., ResNet34 with quantum circuits) and novel approaches (e.g., Quantum Chebyshev Polynomials). Hardware ranged from high-performance GPUs to quantum-specific devices. Performance varied, with accuracy up to 99.5% in some configurations but lower results for complex or limited datasets. Conclusions: The findings provide the first glimpse into the potential of QNNs in MRI, demonstrating accuracy and specificity in diagnostic tasks and biomarker detection. However, challenges such as dataset variability, limited quantum hardware access, and reliance on simulators remain. Future research should focus on scalable quantum hardware, standardized datasets, and optimized architectures to support clinical applications and precision medicine.

Quantum computing is emerging as a transformative tool for communication systems, offering the potential to overcome long-standing physical limitations. In free-space optical networks, orbital angular momentum (OAM) multiplexing promises massive capacity gains, but its practical use is fundamentally constrained by multiphysics degradations such as atmospheric turbulence, volumetric Mie scattering, and stochastic quantum noise. These effects induce nonlinear modal crosstalk and severe beam distortions, against which classical approaches-most notably convolutional neural networks (CNNs)-provide only partial and non-scalable compensation. To address this gap, we report the first use of variational quantum neural networks (QNNs) for adaptive OAM beam compensation in realistic channels. By embedding parameterized entangling layers into a supervised regression pipeline, our QNN achieves end-to-end reconstruction of distorted Laguerre-Gaussian beams with topological charges l ∈ {1,4,8,12}. Using experimentally validated channel parameters, QNNs achieve mean squared error as low as 4.0 × 10- 6, SSIM above 0.99, and bit-error rates suppressed by > 99.9% (0.0125% BER). To ensure scalability, we introduce the quasi-quantum neural network (QqNN), a classical surrogate that emulates quantum dynamics via tensorial projections, achieving near-optimal performance (0.0375% BER) at reduced complexity. This hybrid framework positions QNNs as a quantum-resilient paradigm for OAM decoding and establishes QqNNs as the first scalable surrogate for near-term deployment.

Two-stage behavior of mutual information in quantum neural networks

Abstract Continuous-variable quantum computing (CVQC) uses quantum states with continuous degrees of freedom, such as the quadratures of bosonic modes, to encode information, promising efficient solutions to complex problems. Trapped-ion systems provide a robust platform with long coherence times and precise qubit control, enabling the manipulation of quantum information through its motional and electronic degrees of freedom. In this theoretical work, we quantitatively analyze the fidelity of a Kerr operation in a single trapped-ion system, calibrating the interaction time using a motional-state Rabi frequency correction. Through numerical simulations, we validate Gaussian and non-Gaussian CVQC operations, achieving fidelities exceeding 99% in all cases, including non-Gaussian operations. Furthermore, we demonstrate two key applications: first, the implementation of a continuous-variable quantum neural network for regression problems, which exhibits low error rates; and second, its application to state preparation tasks, achieving a fidelity of 90% for the given example. These results open new opportunities to execute quantum computing algorithms on continuous variables with trapped ions, such as quantum machine learning algorithms.

Energy-efficient routing and predictive sink mobility in mobile wireless sensor networks using reflection equivariant quantum neural network and star fish optimization algorithms

ABSTRACT In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are subject to, and in algorithm design, a large effort is underway to provide scalable error correction or mitigation techniques. Yet some previous work has indicated that certain classes of quantum algorithms, such as quantum machine learning, may, in fact, be intrinsically robust to or even benefit from the presence of a small amount of noise. Here, we demonstrate that noise levels in quantum hardware can be effectively tuned to enhance the ability of quantum neural networks to generalize data, acting akin to regularisation in classical neural networks. As an example, we consider two regression tasks, where, by tuning the noise level in the circuit, we demonstrated improvement of the validation mean squared error loss. Moreover, we demonstrate the method's effectiveness by numerically simulating QNN training on a realistic model of a noisy superconducting quantum computer.

Diabetic retinopathy (DR) is one of the major causes of vision impairment in diabetic patients in the contemporary world. Recently, DR, an aberrant disorder connected to the human retina, has gained international attention. Adults are more likely to have DR, which can result in both minor and significant blindness, as a result of modern humans’ increased daily screen-related activities. Because there are so many patients, doctors and clinicians are unable to make early diagnoses. To address this issue, this research integrates gradient domain-guided filtering for image preprocessing, which guarantees improved noise reduction and edge preservation, and proposes an updated framework for DR classification and detection. The enhanced Mask Region-Based Convolutional Neural Network (Mask R-CNN) is used to get the results in accurate segmentation. Special Reflection Equivariant Quantum Neural Networks (REQNNs) are matched with the Context Axial Reverse Attention Network (CaraNet) to quickly distinguish the features. Optimization is done under the Emperador Penguin Optimizer (EPO), which is known to converge very fast and provide top performance. To assess the effectiveness of the suggested approach, key measures like as area under the curve (AUC), F1-score, recall, accuracy, and precision were calculated using the Messidor-2, APTOS 2019, and EyePACS datasets. The proposed method outperformed a number of cutting-edge baselines, including AdaBoost, TL-CNN, and DenseNet-121, by achieving remarkable results with metrics above 99% on all datasets. These results demonstrate not only the framework’s dependability, stability, and efficacy in detecting DR, but also its potential for practical use in mass screening programs and lowering physician workload. However, the framework’s training demands big, well-annotated datasets, which may limit its usefulness in environments with limited resources. All things considered, the study presents a reliable and precise method for DR classification and detection that can support early intervention and enhance patient outcomes.

Abstract Quantum Machine Learning (QML) presents a novel paradigm for financial modeling, particularly for the challenge of few-shot credit risk assessment, which is a critical issue in inclusive finance where data scarcity limits conventional models. To address this, we propose and implement a hybrid quantum-classical workflow. Our methodology first utilizes a classical model ensemble for dimensionality reduction, creating a dense, three-dimensional feature representation from the original data. This representation then serves as input to a Quantum Neural Network (QNN), trained with the parameter-shift rule, which acts as the core classifier. The framework’s efficacy was validated through numerical simulations and on real hardware using the Quafu Cloud Platform’s ScQ-P21 superconducting processor. On a real-world credit dataset of 279 samples, our QNN achieved a robust average AUC of 0.852 ± 0.027 in simulations and an impressive AUC of 0.89 in the hardware experiment. This performance surpasses a suite of classical benchmarks, with a particularly strong result on the recall metric—crucial for minimizing false negatives in risk control. This study provides a pragmatic blueprint for applying QML to data-constrained financial scenarios and offers valuable empirical evidence of its potential in the NISQ era.