Purification in entanglement distribution with deep quantum neural network

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.

Quantum Machine Learning (QML) is an emerging field at the intersection of quantum computing and machine learning, aiming to enhance classical machine learning methods by leveraging quantum mechanics principles such as entanglement and superposition. However, skepticism persists regarding the practical advantages of QML, mainly due to the current limitations of noisy intermediate-scale quantum (NISQ) devices. This study addresses these concerns by extensively assessing Quantum Neural Networks (QNNs)-quantum-inspired counterparts of Artificial Neural Networks (ANNs), demonstrating their effectiveness compared to classical methods. We systematically construct and evaluate twelve distinct QNN configurations, utilizing two unique quantum feature maps combined with six different entanglement strategies for ansatz design. Experiments conducted on a wind energy dataset reveal that QNNs employing the $\mathbf{Z}$ feature map achieve up to $93 \%$ prediction accuracy when forecasting wind power output using only four input parameters. Our findings show that QNNs outperform classical methods in predictive tasks, underscoring the potential of QML in real-world applications.

The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.

The increasing convergence of quantum computing (QC) and advanced robotic control is giving rise to a new class of intelligent automation systems. Utilizing quantum-inspired computational principles, contemporary robotic platforms demonstrate greater optimization efficiency, superior perceptual processing, and improved decision-making performance. This survey outlines the principal quantum-oriented control methodologies utilized in robotics, with particular emphasis on approaches that incorporate Quantum Neural Networks (QNN), Quantum Machine Learning (QML), and Quantum-behaved Particle Swarm Optimization (QPSO). The investigation systematically reviews recent advances in quantum-assisted adaptive control, trajectory planning, and optimization frameworks, spotlighting their contributions to improved robustness, precision, and energy efficiency. By analyzing research in quantum reinforcement learning, distributed Noisy Intermediate-Scale Quantum (NISQ) computing, and hybrid quantum-classical approaches, this review clarifies how quantum principles are transforming both theoretical and practical aspects of robotic control. Likewise, several real-world implementations ranging from industrial manipulators to autonomous and cognitive robotic systems demonstrate the growing feasibility of quantum-enhanced decision-making. The review concludes that while remarkable progress has been made in quantum-inspired control for robotics, most existing studies remain constrained to simulations with restricted experimental validation on physical platforms. Addressing this gap will be essential in future research to transition from theoretical and simulated models toward hardware-level implementations, enabling the realization of scalable, fault-tolerant quantum control architectures.

Noisy intermediate scale quantum (NISQ) systems are susceptible to errors that culminate in near-one hundred percent data loss. This is due to quantum state fragility and the incredibly high quantum communication error rates caused by decoherence, or quantum noise. As such, stabilizing qubit operational imprecision in quantum information processing is a critical area of research in quantum computing. Adaptive quantum machine learning (QML) methods, like unsupervised and fully entangled quantum generative adversarial networks is one such technology theorized to provide a breakthrough in quantum error suppression. Mechanizing the quantum error detection and correction process with QML provides a path forward from today’s monolithic quantum computers running almost exclusively single-core quantum processing unit (QPU) designs, to the next generation of federated quantum computers using multi-core QPUs. Automating the detection and correction of quantum errors in powerful NISQ devices will pave the way for fault-tolerant quantum computing, making quantum speeds at quantum scale suddenly achievable.

Quantum machine learning stands out as one of the most promising applications of quantum computing, widely believed to possess potential quantum advantages. In the era of noisy intermediate-scale quantum, the scale and quality of quantum computers are limited, and quantum algorithms based on fault-tolerant quantum computing paradigms cannot be experimentally verified in the short term. The variational quantum algorithm design paradigm can better adapt to the practical characteristics of noisy quantum hardware and is currently one of the most promising solutions. However, variational quantum algorithms, due to their highly entangled nature, encounter the phenomenon known as the “barren plateau” during the optimization and training processes, making effective optimization challenging. This paper addresses this challenging issue by researching a variational quantum neural network optimization method based on collective intelligence algorithms. The aim is to overcome optimization difficulties encountered by traditional methods such as gradient descent. We study two typical applications of using quantum neural networks: random 2D Hamiltonian ground state solving and quantum phase recognition. We find that the collective intelligence algorithm shows a better optimization compared to gradient descent. The solution accuracy of ground energy and phase classification is enhanced, and the optimization iterations are also reduced. We highlight that the collective intelligence algorithm has great potential in tackling the optimization of variational quantum algorithms.

Based on the theoretical basis of quantum computation, entanglement has been further explored as one of the key resources. An outstanding problem in quantum computation is the detecting of entanglement, but no closed-form algorithm exists. According to an advanced matrix rearrangement approach for detecting multipartite quantum states, we give some examples to verify the effectiveness and practicability of this new criterion. Meanwhile, this paper shows how techniques from the quantum neural network can be utilized to detect entanglement. Two models, known as the discrete-variable and the continuous-variable quantum neural network, are applied to solve the separability problem. We demonstrate the utility that such a discrete-variable quantum neural network can be trained to detect the entanglement with great exactness. And the complexity of network and computation is greatly reduced. Besides, the continuous-variable quantum neural network is applied for detecting two-qumode Gaussian state. Compared with the results of the traditional neural network, this deep quantum neural network demonstrates its capability and adaptability as well.

Quantum computation promises exponential speedups over classical algorithms, but current Noisy Intermediate-Scale Quantum (NISQ) devices remain highly susceptible to noise. We introduce a Bell-basis computational framework in which each logical qubit is encoded as an entangled pair whose correlation structure enables intrinsic detectability of correlation-breaking errors. Rather than performing explicit recovery or fault-tolerant correction, the scheme implements an intrinsic verification rule that accepts or discards outcomes based on the preservation of Bell-type correlations. A universal logical gate set acting natively in the Bell basis is derived, and Qiskit simulations confirm that correlation violations can be detected with rates of 4–6% under realistic depolarizing and amplitude-damping noise. This approach provides a postselection-based pathway toward verifiable quantum computation on near-term hardware, offering a pragmatic complement to full quantum error correction.

Deep neural networks (DNNs) are state-of-the-art algorithms for multiple applications, spanning from image classification to speech recognition. While providing excellent accuracy, they often have enormous compute and memory requirements. As a result of this, quantized neural networks (QNNs) are increasingly being adopted and deployed especially on embedded devices, thanks to their high accuracy, but also since they have significantly lower compute and memory requirements compared to their floating point equivalents. QNN deployment is also being evaluated for safety-critical applications, such as automotive, avionics, medical or industrial. These systems require functional safety, guaranteeing failure-free behaviour even in the presence of hardware faults. In general fault tolerance can be achieved by adding redundancy to the system, which further exacerbates the overall computational demands and makes it difficult to meet the power and performance requirements. In order to decrease the hardware cost for achieving functional safety, it is vital to explore domain-specific solutions which can exploit the inherent features of DNNs. In this work we present a novel methodology called fault-aware training (FAT), which includes error modeling during neural network (NN) training, to make QNNs resilient to specific fault models on the device. Our experiments show that by injecting faults in the convolutional layers during training, highly accurate convolutional neural networks (CNNs) can be trained which exhibits much better error tolerance compared to the original. Furthermore, we show that redundant systems which are built from QNNs trained with FAT achieve higher worse-case accuracy at lower hardware cost. This has been validated for numerous classification tasks including CIFAR10, GTSRB, SVHN and ImageNet.

The noisy intermediate-scale quantum devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the representation and generalization powers of VQC still require further investigation, particularly when the dimensionality of classical inputs is concerned. In this work, we first put forth an end-to-end QNN, TTN-VQC, which consists of a quantum tensor network based on a tensor-train network (TTN) for dimensionality reduction and a VQC for functional regression. Then, we aim at the error performance analysis for the TTN-VQC in terms of representation and generalization powers. We also characterize the optimization properties of TTN-VQC by leveraging the Polyak-Lojasiewicz condition. Moreover, we conduct the experiments of functional regression on a handwritten digit classification dataset to justify our theoretical analysis.

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.

Quantum computing is emerging as a powerful computational paradigm capable of solving infeasible problems for classical computers. This review explores the intersection of quantum computing and artificial intelligence (AI), focusing on how quantum algorithms can enhance AI applications. The purpose of this review is to provide a comprehensive analysis of current advancements in quantum machine learning (QML), quantum optimization, and quantum neural networks, highlighting their implications for data processing, cryptography, and decision-making systems. The scope of the literature includes peer-reviewed articles, conference papers, and technical reports from 2020 to 2025, focusing on quantum algorithms, applications in AI, and hardware limitations. Key findings indicate that quantum computing can significantly accelerate data processing tasks, optimize complex problem-solving techniques, and improve the efficiency of AI models. However, challenges such as quantum noise, error correction, and hardware scalability remain substantial barriers to widespread adoption. This review concludes with discussing future research directions, including hybrid quantum-classical systems and advanced quantum error correction methods. This study serves as a foundational reference for researchers and practitioners aiming to leverage quantum computing for AI-driven applications. 3. Keywords Quantum Computing, Artificial Intelligence, Quantum Machine Learning, Quantum Algorithms, Data Processing, Optimization, Quantum Neural Networks

Alzheimer's disease (AD) presents significant diagnostic challenges owing to the subtle morphological similarities observed in the early stages, with traditional deep learning approaches often struggling to distinguish between the various stages of disease progression via structural Magnetic Resonance Imaging (MRI) data. Quantum computing offers unique advantages for medical image analysis, leveraging superposition and entanglement capabilities to process high-dimensional feature spaces beyond the limits of classical computation. This study introduces a hybrid quantum-classical neural network architecture (HQC-Net) for accurate four-class Alzheimer's disease classification, which uses quantum processing to detect patterns that are often invisible to classical spatial analysis methods. The proposed framework integrates classical feature extractors, including a custom CNN and modified ResNet18, with six-qubit variational quantum circuits that employ multiaxis rotation encoding (RY→RZ→RX), a quantum Fourier transform for spectral decomposition, and multihead attention for effective quantum-classical feature fusion. Comprehensive evaluations were conducted on the Kaggle dataset (5,121 samples) and the OASIS dataset (20,000 samples), incorporating realistic quantum noise modelling, including depolarising, amplitude damping, and phase damping channels. The modified QResNet18 configuration achieved a test accuracy of 99.67%, with perfect discriminative capability (AUC = 1.0000) on the OASIS dataset. Quantum processing demonstrated superior detection of very mild dementia (99.86% accuracy), which is crucial for early intervention. The proposed approach outperformed existing quantum-enhanced methods by 3.57 percentage points while effectively handling the increased diagnostic complexity associated with four-class classification. This study demonstrates a practical quantum advantage for multiclass neuroimaging classification, achieving superior diagnostic accuracy while maintaining computational efficiency and clinical deployment feasibility under current Noisy Intermediate-Scale Quantum (NISQ) hardware constraints.

Quantum kernel methods have been widely recognized as one of the promising quantum machine learning (QML) algorithms that have the potential to achieve quantum advantages. However, their capabilities may be severely degraded by inevitable noises in the current noisy intermediate-scale quantum (NISQ) era. In this article, we theoretically characterize the power of noisy quantum kernels and demonstrate that under depolarizing noise, quantum kernel methods may only have very poor prediction capability, even when the generalization error is small. Specifically, we quantitatively describe the decreasing of the prediction capability of noisy quantum kernels in terms of the rate of quantum noise, the size of training samples, the number of qubits, and the number of layers affected by quantum noises. Our results clearly demonstrate that for a given number of training samples, once the number of layers affected by noise exceeds some threshold, the prediction capability of noisy kernels is very poor. Thus, we provide a crucial warning to employ noisy quantum kernel methods for quantum computation and the theoretical results can also serve as guidelines when developing practical quantum kernel algorithms for achieving quantum advantages.

Machine learning has surged in popularity in recent years, with deep neural networks (DNNs) becoming a cornerstone of applications such as autonomous driving, augmented reality, and natural language processing, owing to their remarkable accuracy and scalability. As the demand for greater portability and flexibility grows, there is a strong push to optimize these applications for resource-constrained edge devices like smartphones and IoT devices.However, deploying DNN models on such devices presents significant challenges, primarily due to the large size of these models, which is a key contributor to their high performance. For instance, the DeepSpeech 2 model outperforms its predecessor, DeepSpeech 1, but its size is eight times larger, encompassing approximately 68 million parameters. Similarly, other networks designed for various tasks, including convolutional neural networks like VGG and transformer-based networks like BERT and GPT, also exhibit substantial sizes. For example, the GPT-3 model, a predecessor to ChatGPT, consists of an astonishing 175 billion parameters. Consequently, fitting DNN models onto resource-limited edge devices is a formidable challenge. My thesis addresses these challenges with a three-part approach: * High-Performance DNN Accelerators: I will develop DNN accelerators that excel in high performance, low latency, and energy efficiency through an algorithm and hardware co-design across diverse FPGA architectures (Chapter 2). * Real-Time DNN Execution: I aim to achieve exceptional accuracy and real-time execution for various large-scale DNNs on off-the-shelf mobile devices, IoT devices, and other platforms (Chapter 3). * CompVQC Framework: I will explore a systematic framework, CompVQC, to reduce the circuit length of quantum neural networks (QNNs) through model compression, which can achieve up to a 20% improvement in accuracy. This reveals that compilation-aware compression can enhance the robustness of QNNs on near-term noisy quantum devices (Chapter 4). The field of AI has recently undergone a significant transformation, ushering in the era of generative AI, where models like ChatGPT and Stable Diffusion create realistic and creative content for a wide range of applications. As generative AI becomes more prevalent, it is crucial to adapt algorithm-hardware co-design strategies to meet the specific needs of these models, particularly on edge devices. In the final chapter (Chapter 5), I will introduce my ongoing and future work focused on activating generative AI on the edge.--Author's abstract