The field of quantum neural networks, an emerging interdisciplinary frontier bridging quantum computing and machine learning, has recently garnered substantial attention in the scientific community. In this work, we propose a complex-valued quantum neural network in the quantum circuit framework through expanding the number domains of conventional quantum machine learning architecture from the real-valued domain to the complex-valued plane. Such an expansion can alleviate the unitary constraints in quantum feature maps and optimization blocks, and introduce enhanced nonlinear characteristics. It is proven theoretically that the expressivity can be significantly enhanced through the frequency-dependent adaptability and the exponential or hyperbolic functional distribution extension for the Fourier coefficients of quantum models' outputs. Moreover, analysis based on covering numbers indicates that our algorithm can achieve an adaptive balance between expressivity and generalization via the trainable scaling factor, while exhibiting superior parameter efficiency relative to unitary quantum learning models. The performance of the proposed algorithms is demonstrated through extensive numerical simulations in regression and classification tasks, including an experimental realization on the superconducting quantum processor. Our work advances the harnessing of imaginarity resources of quantum theory for learning tasks, achieving a theoretically grounded performance enhancement, and underscores the potential of improving quantum neural networks through structured design for future applications.
The field of quantum neural networks, an emerging interdisciplinary frontier bridging quantum computing and machine learning, has recently garnered substantial attention in the scientific community. In this work, we propose a complex-valued quantum neural network in the quantum circuit framework through expanding the number domains of conventional quantum machine learning architecture from the real-valued domain to the complex-valued plane. Such an expansion can alleviate the unitary constraints in quantum feature maps and optimization blocks, and introduce enhanced nonlinear characteristics. It is proven theoretically that the expressivity can be significantly enhanced through the frequency-dependent adaptability and the exponential or hyperbolic functional distribution extension for the Fourier coefficients of quantum models' outputs. Moreover, analysis based on covering numbers indicates that our algorithm can achieve an adaptive balance between expressivity and generalization via the trainable scaling factor, while exhibiting superior parameter efficiency relative to unitary quantum learning models. The performance of the proposed algorithms is demonstrated through extensive numerical simulations in regression and classification tasks, including an experimental realization on the superconducting quantum processor. Our work advances the harnessing of imaginarity resources of quantum theory for learning tasks, achieving a theoretically grounded performance enhancement, and underscores the potential of improving quantum neural networks through structured design for future applications.
In recent years, there has been remarkable progress in improving the availability of resources and refining algorithms for quantum computing. Since the late 1980s, the scientific community has been fascinated by the idea of harnessing quantum phenomena to tackle computational problems. This article provides a comprehensive exploration of the foundational theories and practical applications of quantum neural networks (QNNs), highlighting their potential to transform machine learning through unique features like quantum parallelism and entanglement. It delves into various QNN architectures, such as quantum circuits and hybrid quantum-classical models, showcasing their effectiveness in handling intricate computational tasks more efficiently than traditional neural networks. Furthermore, the article examines the current challenges and future prospects in this rapidly advancing field, emphasizing the pivotal role of QNNs in driving forward research in both quantum computing and artificial intelligence. Quantum neural networks are poised to not only enhance computational capabilities but also pave the way for groundbreaking innovations in diverse technological domains.
Abstract In noisy intermediate-scale quantum era, the research on the combination of artificial intelligence and quantum computing has been greatly developed. Here we propose a quantum circuit-based algorithm to implement quantum residual neural networks, where the residual connection channels are constructed by introducing auxiliary qubits to data-encoding and trainable blocks in quantum neural networks. We prove that when this particular network architecture is applied to a l -layer data-encoding, the number of frequency generation forms extends from one, namely the difference of the sum of generator eigenvalues, to O(l2) O ( l 2 ) , and the flexibility in adjusting Fourier coefficients can also be improved. It indicates that residual encoding can achieve better spectral richness and enhance the expressivity of various parameterized quantum circuits. Extensive numerical demonstrations in regression tasks and image classification are offered. Our work lays foundation for the complete quantum implementation of classical residual neural networks and offers a quantum feature map strategy for quantum machine learning.
Quantum Neural Networks (QNNs) have emerged as a promising avenue in the quest for next-generation machine learning capabilities.By harnessing the principles of quantum mechanics and quantum computing, QNNs offer the potential for exponential speedup and enhanced computational power compared to classical machine learning algorithms.This paper presents a comprehensive exploration of Quantum Neural Networks, covering their foundational concepts, various architectures, novel quantum-enhanced machine learning algorithms, practical implementations, advantages, and challenges.We begin with an overview of related work in Quantum Machine Learning, highlighting the achievements and progress in the field.Subsequently, we delve into the fundamental principles of Quantum Mechanics and Quantum Computing to provide a solid grounding for understanding QNNs.We then introduce the basics of Quantum Neural Networks, including quantum neurons, quantum gates, and quantum circuits for machine learning tasks.Various QNN architectures, such as Variational Quantum Circuits and Quantum Convolutional Neural Networks, are explored along with their potential applications.Additionally, quantum-enhanced machine learning algorithms, like Quantum Support Vector Machines and Quantum Generative Adversarial Networks, are discussed for a deeper understanding of QNN capabilities.Practical aspects, including hardware implementations, noise mitigation, and experimental results, are presented to shed light on the feasibility of QNNs in real-world scenarios.The paper concludes by discussing the advantages and challenges of Quantum Neural Networks and their potential implications for the future of machine learning and artificial intelligence.
Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power enables the development of sophisticated models and training strategies, leading to state-of-the-art performance, but it also introduces substantial challenges. Quantum Computing (QC), which exploits quantum mechanisms for computation, has attracted growing attention and significant global investment as it may address these challenges. Consequently, Quantum Machine Learning (QML), the integration of these two fields, has received increasing interest, with a notable rise in related studies in recent years. We are motivated to review these existing contributions regarding quantum circuit-based learning models for classical data analysis and highlight the identified potentials and challenges of this technique. Specifically, we focus not only on QML models, both kernel-based and neural network-based, but also on recent explorations of their integration with classical machine learning layers within hybrid frameworks. Moreover, we examine both theoretical analysis and empirical findings to better understand their capabilities, and we also discuss the efforts on noise-resilient and hardware-efficient QML that could enhance its practicality under current hardware limitations. In addition, we cover several emerging paradigms for advanced quantum circuit design and highlight the adaptability of QML across representative application domains. This study aims to provide an overview of the contributions made to bridge quantum computing and machine learning, offering insights and guidance to support its future development and pave the way for broader adoption in the coming years.
This paper presents the concept of quantum neural networks (QNN), a new framework that combines quantum computing with topological data analysis to process data defined on simplicial complexes. Based on the fundamentals of topological signal processing and variational quantum circuits, QNN aim to use the structure of simplicial complexes to perform efficient calculations and extract higher-order relational patterns from data. The proposed architecture uses quantum layers (QL), which map interactions between simplices into quantum circuits, providing both in-order and inter-order interactions. The paper describes two QL variants: basic and schematic, providing flexibility for applications with varying complexity. In addition, the paper explores the theoretical foundations of simplicial complexes, quantum neural networks, and the interaction between classical and quantum approaches in data encoding, state evolution and optimization. By leveraging quantum algorithms and eliminating current hardware limitations, QNN promise scalability and enhanced performance for applications in optimization, numerical simulation, and complex systems modeling. This research demonstrates the potential of QNN to advance the field of quantum machine learning, paving the way for future developments of quantum algorithms and their practical applications.
Recent advances in Machine Learning have transformed numerous industrial sectors, yet classical paradigms face fundamental limitations: rapidly growing data volumes, rising computational costs, significant energy consumption, and the physical scaling limits of conventional hardware architectures. Quantum computing has emerged as a promising computational paradigm to address these challenges, giving rise to the field of Quantum Machine Learning (QML). In this thesis, the theoretical foundations of QML are investigated, with a focus on near-term and future practical applications. Three central challenges are addressed: the trainability of variational quantum circuits, their expressivity, and their resistance to efficient classical simulation. The trainability of Hamming-weight preserving variational quantum circuits is first studied, and theoretical guarantees are established that resolve an open conjecture on the absence of barren plateaus for this circuit family. Subspace-preserving QML algorithms are then introduced, including photonic circuits and quantum convolutional neural networks, and are designed to mimic classical ML subroutines while offering polynomial quantum advantage. Finally, variational quantum circuits are analyzed as quantum Fourier models, and a framework is derived to jointly characterize expressivity and trainability, from which conditions are obtained under which quantum models provably separate from their classical counterparts. These contributions are intended to advance the theoretical roadmap for harnessing near-term and future quantum technologies in real-world applications.