Quantum vs. Classical Machine Learning: A Unified Empirical Comparison

The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new paradigm. This paper presents a comprehensive benchmarking study of classical and quantum machine learning models for image recognition on the MNIST handwritten digit dataset, evaluating both traditional models, a Classical Support Vector Machine (CSVM) and a Quantum Support Vector Machine (QSVM), and deep neural network models, a Classical Convolutional Neural Network (CCNN) and a Quantum Convolutional Neural Network (QCNN), across four performance dimensions: classification accuracy, computational runtime, parameter count, and memory requirements. Experiments are conducted as functions of both feature dimensionality and sample size, and across CPU and GPU execution environments, providing a controlled, multidimensional comparison to address gaps in prior work. For the SVM-based models, QSVM consistently outperforms CSVM in accuracy, reaching $\sim$ 0.90 versus $\sim$ 0.85 at 1,000 samples, with a higher computational cost. A feature count of 10 qubits and a sample size in the range of 200 -- 500 emerge as practical operating points that balance accuracy and runtime. For the neural network models, CCNN and QCNN achieve comparable classification accuracy, both exceeding 0.96 at 64 features and 60,000 samples, yet QCNN offers substantially superior parameter and memory efficiency, requiring $\sim$ 94% fewer parameters and $\sim$ 75% less memory than CCNN at higher feature counts, while incurring higher runtime. Across both model families, quantum models consistently outperform classical models by greater margins in accuracy as feature dimensionality or sample size increases.

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.

Quantum Machine Learning (QML) has shown rapid advances by utilizing quantum computing for machine learning tasks. Meanwhile, the privacy risks accompanying QML is also starting to be studied, which inherit privacy leakage channels from "classical" ML and also quantum-unique risks. Existing work on privacy-preserving QML largely focuses on a QML-as-a-service scenario, which generally assumes that the QML model owner provides only classical bit outputs to queries, while users (and adversaries) have only classical computing abilities. However, this view is increasingly challenged in a quantum-native world of quantum-capable users/adversaries, which may have access to both quantum computing abilities and access to quantum information output from service providers. In this paper, we aim to bridge this gap by examining membership inference attacks against QML models by demonstrating that increasing quantum access and quantum computing abilities provides provable theoretical privacy leakage and empirical adversarial gain. However, the probabilistic nature of QML introduces a gap between theoretical and empirical adversarial advantage. These results show that existing research on privacy leakage in QML models underestimates privacy leakage in emergent quantum-native access regimes, and we hope to establish a first step in examining potential privacy leakages for QML in the quantum-native world.