Quantum machine learning, which involves running machine learning algorithms on quantum devices, may be one of the most significant flagship applications for these devices. Unlike its classical counterparts, the role of data in quantum machine learning has not been fully understood. In this work, we quantify the performances of quantum machine learning in the landscape of quantum data. Provided that the encoding of quantum data is sufficiently random, the performance, we find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in the number of qubits, which we call "the curse of random quantum data". Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks. Conversely, we highlight that through meticulous design of quantum datasets, it is possible to avoid these curses, thereby achieving efficient convergence and robust generalization. Our conclusions are corroborated by extensive numerical simulations.
Quantum machine learning, which involves running machine learning algorithms on quantum devices, may be one of the most significant flagship applications for these devices. Unlike its classical counterparts, the role of data in quantum machine learning has not been fully understood. In this work, we quantify the performances of quantum machine learning in the landscape of quantum data. Provided that the encoding of quantum data is sufficiently random, the performance, we find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in the number of qubits, which we call "the curse of random quantum data". Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks. Conversely, we highlight that through meticulous design of quantum datasets, it is possible to avoid these curses, thereby achieving efficient convergence and robust generalization. Our conclusions are corroborated by extensive numerical simulations.
Abstract Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum kernels are impractical for large datasets as they scale with the square of the dataset size. Here, we measure quantum kernels using randomized measurements. The quantum computation time scales linearly with dataset size and quadratic for classical post-processing. While our method scales in general exponentially in qubit number, we gain a substantial speed-up when running on intermediate-sized quantum computers. Further, we efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth. The encoding is characterized by the quantum Fisher information metric and is related to the radial basis function kernel. Our approach is robust to noise via a cost-free error mitigation scheme. We demonstrate the advantages of our methods for noisy quantum computers by classifying images with the IBM quantum computer. To achieve further speedups we distribute the quantum computational tasks between different quantum computers. Our method enables benchmarking of quantum machine learning algorithms with large datasets on currently available quantum computers.
Quantum machine learning (QML) is the spearhead of quantum computer applications. In particular, quantum neural networks (QNN) are actively studied as the method that works both in near-term quantum computers and fault-tolerant quantum computers. Recent studies have shown that supervised machine learning with QNN can be interpreted as the quantum kernel method (QKM), suggesting that enhancing the practicality of the QKM is the key to building near-term applications of QML. However, the QKM is also known to have two severe issues. One is that the QKM with the (inner-product based) quantum kernel defined in the original large Hilbert space does not generalize; namely, the model fails to find patterns of unseen data. The other one is that the classical computational cost of the QKM increases at least quadratically with the number of data, and therefore, QKM is not scalable with data size. This paper aims to provide algorithms free from both of these issues. That is, for a class of quantum kernels with generalization capability, we show that the QKM with those quantum kernels can be made scalable by using our proposed deterministic and random features. Our numerical experiment, using datasets including O(1,000)∼O(10,000) training data, supports the validity of our method.
Abstract - The exponential growth of large-scale data has created significant challenges in storage, processing, and optimization that classical computing systems struggle to address efficiently. Quantum Machine Learning (QML) has emerged as a promising paradigm that integrates quantum computing concepts with machine learning techniques to tackle complex big data optimization problems. By utilizing quantum features such as superposition, entanglement, and parallelism, QML algorithms can accelerate tasks like clustering, classification, and dimensionality reduction, which are traditionally computationally demanding. Recent advancements indicate strong potential for quantum-inspired optimization in fields including cybersecurity, financial portfolio management, Industry 4.0, and healthcare analytics. This paper provides a comprehensive survey of QML algorithms designed for big data optimization, examining their advantages, limitations, and application domains. Additionally, it discusses the performance trade-offs associated with hybrid quantum–classical frameworks and highlights future research directions aimed at creating secure, scalable, and resource-efficient quantum solutions for large-scale, data-driven decision-making. As data volumes continue to expand at extremely rapid rates, processing big data with traditional machine learning (ML) techniques has become increasingly challenging. ML models often struggle with issues related to computational power, efficient parameter tuning, accurate model selection, and maintaining high performance when dealing with massive datasets. Deep learning approaches—such as convolutional neural networks (CNNs)—demand substantial computational resources to train on large-scale supervised learning tasks. Moreover, the difficulty of training these networks grows significantly as the size and complexity of the datasets increase. In response to these limitations, Quantum Machine Learning (QML) has emerged as a promising research domain at the intersection of quantum computing and machine learning. Quantum computers operate fundamentally differently from classical systems, using the principles of quantum mechanics to encode and process information. As a result, quantum computational methods have the potential to address certain problems that are computationally intensive or infeasible for classical machines. Index Terms— Quantum Machine Learning (QML); Big Data Optimization; Quantum Algorithms; Hybrid Quantum-Classical Models; Quantum Computing; Data Analytics
The importance of analyzing nontrivial datasets when testing quantum machine learning (QML) models is becoming increasingly prominent in literature, yet a cohesive framework for understanding dataset characteristics remains elusive. In this work, we concentrate on the size of the dataset as an indicator of its complexity and explores the potential for QML models to demonstrate superior data-efficiency compared to classical models, particularly through the lens of quantum kernel methods (QKMs). We provide a method for generating semi-artificial fully classical datasets, on which we show one of the first evidence of the existence of classical datasets where QKMs require less data during training. Additionally, our study introduces a new analytical tool to the QML domain, derived for classical kernel methods, which can be aimed at investigating the classical-quantum gap. Our empirical results reveal that QKMs can achieve low error rates with less training data compared to classical counterparts. Furthermore, our method allows for the generation of datasets with varying properties, facilitating further investigation into the characteristics of real-world datasets that may be particularly advantageous for QKMs. We also show that the predicted performance from the analytical tool we propose - a generalization metric from classical domain - show great alignment empirical evidence, which fills the gap previously existing in the field. We pave a way to a comprehensive exploration of dataset complexities, providing insights into how these complexities influence QML performance relative to traditional methods. This research contributes to a deeper understanding of the generalization benefits of QKM models and potentially a broader family of QML models, setting the stage for future advancements in the field.
Quantum machine learning methods, including quantum kernels and variational quantum algorithms (VQAs), are poised to demonstrate quantum advantages in machine learning, chemistry, condensed matter physics, and materials science. However, these methods face critical challenges hindering practical quantum advantates: quantum kernels require meticulous design to outperform classical alternatives, while VQA training is obstructed by barren plateaus (BPs) in the optimization landscape. To address these issues, this thesis proposes two novel frameworks to guide quantum kernel design and tackle quantum neural network (QNN) training challenges in VQAs. Specifically, to resolve quantum kernel design challenges, we propose a data-driven method for automatic quantum kernel design, leveraging classical machine learning to learn from input data and identify optimal kernel structures. Experiments show this method finds suitable quantum kernels that avoid vanishing similarity, a common flaw in traditional designs. To improve VQA trainability, we propose an encoder-decoder parameter prediction framework, where a graph neural network (GNN) acts as the encoder to process information based on the QNN’s directed acyclic graph (DAG). Experiments confirm the parameters from this framework significantly enhance VQAs’ robustness, convergence speed, and trainability. In conclusion, we propose two schemes, QuKerNet and QuGHN, for automatic quantum kernel design and enhanced VQA trainability. QuKerNet considers optimal circuit layouts and variational parameters, and is more resource-efficient for contemporary quantum hardware by accounting for qubit topology and count. QuGHN is versatile, applicable to circuits with varying qubits, ansatzes, and tasks; its parameters enable faster convergence and more stable VQA solutions. These advancements enhance quantum machine learning practicality on near-term machines and its utility in large-scale quantum circuit simulations.
The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits.