Abstract The rapid development of quantum computers promises transformative impacts across diverse fields of science and technology. Quantum neural networks (QNNs), as a forefront application, hold substantial potential. Despite the multitude of proposed models in the literature, persistent challenges, notably the vanishing gradient (VG) and cost function concentration (CFC) problems, impede their widespread success. In this study, we introduce a novel approach to quantum neural network construction, specifically addressing the issues of VG and CFC.Our methodology employs ensemble learning, advocating for the simultaneous deployment of multiple quantum circuits with a depth equal to 1, a departure from the conventional use of a single quantum circuit with depth L. We assess the efficacy of our proposed model through a comparative analysis with a conventionally constructed QNN. The evaluation unfolds in the context of a classification problem, yielding valuable insights into the potential advantages of our innovative approach.
Abstract The rapid development of quantum computers promises transformative impacts across diverse fields of science and technology. Quantum neural networks (QNNs), as a forefront application, hold substantial potential. Despite the multitude of proposed models in the literature, persistent challenges, notably the vanishing gradient (VG) and cost function concentration (CFC) problems, impede their widespread success. In this study, we introduce a novel approach to quantum neural network construction, specifically addressing the issues of VG and CFC.Our methodology employs ensemble learning, advocating for the simultaneous deployment of multiple quantum circuits with a depth equal to 1, a departure from the conventional use of a single quantum circuit with depth L. We assess the efficacy of our proposed model through a comparative analysis with a conventionally constructed QNN. The evaluation unfolds in the context of a classification problem, yielding valuable insights into the potential advantages of our innovative approach.
Abstract The barren plateau problem in quantum neural networks (QNNs) is a significant challenge that hinders the practical success of QNNs. In this paper, we introduce residual quantum neural networks (ResQNets) as a solution to address this problem. ResQNets are inspired by classical residual neural networks and involve splitting the conventional QNN architecture into multiple quantum nodes, each containing its own parameterized quantum circuit, and introducing residual connections between these nodes. Our study demonstrates the efficacy of ResQNets by comparing their performance with that of conventional QNNs and plain quantum neural networks through multiple training experiments and analyzing the cost function landscapes. Our results show that the incorporation of residual connections results in improved training performance. Therefore, we conclude that ResQNets offer a promising solution to overcome the barren plateau problem in QNNs and provide a potential direction for future research in the field of quantum machine learning.
While Quantum Convolutional Neural Networks (QCNNs) offer a theoretical paradigm for quantum machine learning, their practical implementation is severely bottlenecked by barren plateaus -- the exponential vanishing of gradients -- and poor empirical accuracy compared to classical counterparts. In this work, we propose a novel QCNN architecture utilizing localized cost functions and a hardware-efficient tensor-network initialization strategy to provably mitigate barren plateaus. We evaluate our scalable QCNN on the MNIST dataset, demonstrating a significant performance leap. By resolving the gradient vanishing issue, our optimized QCNN achieves a classification accuracy of 98.7\%, a substantial improvement over the baseline QCNN accuracy of 52.32\% found in unmitigated models. Furthermore, we provide empirical evidence of a parameter-efficiency advantage, requiring O(logN) fewer trainable parameters than equivalent classical CNNs to achieve >95% convergence. This work bridges the gap between theoretical quantum utility and practical application, providing a scalable framework for quantum computer vision tasks without succumbing to loss landscape concentration.
This research explores the development of Quantum Neural Networks (QNNs) as a transformative approach for complex data classification. Utilizing a numerical example, we illustrate the foundational quantum principles of superposition and entanglement within QNNs. The hybrid quantum-classical processing paradigm is introduced, emphasizing the seamless integration of quantum and classical components, acknowledging the challenges of quantum error correction and noise in Noisy Intermediate-Scale Quantum (NISQ) devices. While the example is deliberately simple, it serves as a starting point for understanding the unique advantages and challenges associated with QNNs. Our findings highlight the potential of quantum computation for parallel processing but also underscore the need to address current limitations for practical applications. Future research directions include investigating sophisticated quantum circuits, exploring error mitigation strategies, and assessing QNN performance across diverse datasets. Collaboration between quantum computing and machine learning communities is essential for the advancement of QNNs, and developments in quantum hardware will play a pivotal role in realizing their full potential. This study contributes to the evolving discourse at the intersection of quantum computing and machine learning, providing foundational insights and laying the groundwork for further exploration in this rapidly advancing field.
Barren Plateaus are a formidable challenge for hybrid quantum-classical algorithms that lead to flat plateaus in the loss function landscape making it difficult to take advantage of the expressive power of parameterized quantum circuits with gradient-based methods. Like in classical neural network models, parameterized quantum circuits suffer the same vanishing gradient issue due to large parameter spaces with non-convex landscapes. In this review, we present an overview of the different genesis for barren plateaus, mathematical formalisms of common themes around barren plateaus, and dives into gradients. The central objective is to provide a conceptual perspective between classical and quantum interpretations of vanishing gradients as well as dive into techniques involving cost functions, entanglement, and initialization strategies to mitigate barren plateaus. Addressing barren plateaus paves the way towards feasibility of many classically intractable applications for quantum simulation, optimization, chemistry, and quantum machine learning.
The field of machine learning has experienced rapid development over the last decades and has found numerous applications across diverse domains ranging from industrial to personal settings. Quantum computing, on the other hand, is an emerging field offering a fundamentally different computational paradigm that can potentially surpass traditional computational approaches in certain domains.In this thesis, we explore the intersection between these two fields, commonly referred to as quantum machine learning (QML). In particular, we focus on Quantum neural networks (QNNs), which have gained attention in the field of QML due to the unparalleled success of their classical counterparts. However, the limitations of the current quantum computers have led to hybrid approaches combining classical and quantum devices. We, therefore, use hybrid quantum neural networks (HQNNs) to explore the potential advantages of QNNs in various practical applications.First, we explore the design space of HQNNs as there is no standardized methodology for designing quantum layers in HQNNs. Various quantum layer designs with different data encoding techniques are investigated, identifying the optimal set of quantum gates for different encoding strategies.We also investigate the impact of cost function globality and locality on the performance of HQNNs for real-world applications, namely: binary and multi-class classification. We exploit a single parameterized quantum circuit (PQC) structure with both single (local) and all-qubit (global) measurements. Our results show that the global cost function significantly outperforms the local cost function on multi-class classification. In contrast, both global and local cost functions have comparable performance on binary classification problems.Moreover, we propose a framework for analyzing the impact of various components of HQNNs with respect to each other on multi-class classification tasks, specifically focusing on the data encoding and quantum layers (expressibility and entanglement between qubits). Two ansatz structures, entangled and unentangled, are used to investigate the existence of the barren plateau (BP) in HQNNs. We further evaluate the impact of entanglement on trainability and provide recommendations for different constraint scenarios. The results show that the overall expressibility of the quantum layers impacts the presence of the BP phenomenon and that entanglement plays a role in the training landscapes of HQNNs, depending on the data encoding technique. Finally, we propose a new architecture for quantum neural networks (QNNs) called residual quantum neural networks (ResQNets), inspired by the classical residual neural networks (ResNets), to address the issue of BP in QNNs. ResQNets split the conventional QNN architecture into multiple quantum nodes (QNs), each with its own PQC, allowing residual connections between QNs. The results show that incorporating residual connections results in improved training performance, making ResQNets a promising solution for overcoming the problem of BP in QNNs.
In recent years, quantum computing has emerged as a potentially gamechanging technology, with applications across various disciplines, including AI and machine learning.In recent years, the combination of quantum computing and neural networks has led to the development of quantum neural networks (QNNs).This paper explores the potential of QNNs and their applications in solving complex problems that are challenging for classical neural networks.This paper explores the fundamental principles of quantum computing, the architecture of QNNs, and their advantages over classical neural networks.Furthermore, this will highlight key research areas and challenges in the development and utilization of QNNs.Through an in-depth analysis, it demonstrates the QNNs hold significant promise for addressing complex computational problems and advancing the field of artificial intelligence.