The rapidly emerging paradigms of quantum machine learning (QML) and variational quantum computing (VQC) promise to combine quantum computational advantages with the powerful capabilities of machine learning and optimization. However, early attempts to naively translate classical machine learning techniques into the quantum domain have encountered severe scalability bottlenecks, both practical and theoretical. This dissertation posits that overcoming these limitations requires a fundamental shift in model and algorithm design: the deliberate integration of inductive bias. By embedding task-specific prior knowledge into quantum models and optimization strategies, this research demonstrates how to achieve the scalability required for near-term real-world applications and long-term success towards quantum advantage. This dissertation demonstrates the power of inductive bias across four methodological contributions. First, fast, gradient-free parameter and ansatz optimizers are developed to bypass costly gradient estimation on quantum computers. By explicitly embedding restriction and implicit biases into the quantum circuit ansatz and optimization method, these algorithms drastically improve resource efficiency, scaling variational quantum eigensolvers for molecular chemistry and quantum feature-map learning for classical data. Second, building on this scalable processing of high-dimensional classical data for discriminative tasks, the dissertation advances generative QML. To achieve high-quality, diverse real-world image generation, a quantum generator is designed with a strong, explicit inductive bias toward visual data, structurally reflecting both spatial image features and distribution characteristics. Third, complementary to learning from classical data, the dissertation advances QML for quantum data, processing inputs directly as quantum states rather than classical vectors. Here, a quantum Gaussian process paradigm is established, deriving a physics-informed inductive bias by encoding quantum information-theoretic assumptions. This bias guarantees provable model faithfulness and theoretical scalability. Finally, to ground this theoretical framework in physical reality, it is demonstrated on regression, classification, and optimization tasks, particularly for physical models. These physical applications close the loop to the initial quantum chemistry research, reinforcing both the overarching necessity and the natural presence of domain-specific inductive bias. Overall, the dissertation delivers timely and relevant findings that advance QML and VQC for near-term practical applications, while laying a foundation for the long-term perspective of quantum computing at scale.
The rapidly emerging paradigms of quantum machine learning (QML) and variational quantum computing (VQC) promise to combine quantum computational advantages with the powerful capabilities of machine learning and optimization. However, early attempts to naively translate classical machine learning techniques into the quantum domain have encountered severe scalability bottlenecks, both practical and theoretical. This dissertation posits that overcoming these limitations requires a fundamental shift in model and algorithm design: the deliberate integration of inductive bias. By embedding task-specific prior knowledge into quantum models and optimization strategies, this research demonstrates how to achieve the scalability required for near-term real-world applications and long-term success towards quantum advantage. This dissertation demonstrates the power of inductive bias across four methodological contributions. First, fast, gradient-free parameter and ansatz optimizers are developed to bypass costly gradient estimation on quantum computers. By explicitly embedding restriction and implicit biases into the quantum circuit ansatz and optimization method, these algorithms drastically improve resource efficiency, scaling variational quantum eigensolvers for molecular chemistry and quantum feature-map learning for classical data. Second, building on this scalable processing of high-dimensional classical data for discriminative tasks, the dissertation advances generative QML. To achieve high-quality, diverse real-world image generation, a quantum generator is designed with a strong, explicit inductive bias toward visual data, structurally reflecting both spatial image features and distribution characteristics. Third, complementary to learning from classical data, the dissertation advances QML for quantum data, processing inputs directly as quantum states rather than classical vectors. Here, a quantum Gaussian process paradigm is established, deriving a physics-informed inductive bias by encoding quantum information-theoretic assumptions. This bias guarantees provable model faithfulness and theoretical scalability. Finally, to ground this theoretical framework in physical reality, it is demonstrated on regression, classification, and optimization tasks, particularly for physical models. These physical applications close the loop to the initial quantum chemistry research, reinforcing both the overarching necessity and the natural presence of domain-specific inductive bias. Overall, the dissertation delivers timely and relevant findings that advance QML and VQC for near-term practical applications, while laying a foundation for the long-term perspective of quantum computing at scale.
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 sits at the intersection of two paradigm-shifting technologies: quantum computing and deep learning. By exploiting quantum mechanical phenomena – superposition, entanglement, and interference – QML promises exponential or quadratic speedups over classical algorithms for certain learning tasks, as well as the ability to model quantum data natively. However, the path to practical quantum advantage remains contested, constrained by noisy intermediate-scale quantum (NISQ) hardware, limited qubit counts (50–1,000), coherence times (50–500 μs), and high gate error rates (10⁻³–10⁻⁴). This paper provides a rigorous, technically deep survey of QML: mathematical foundations (Hilbert spaces, unitary evolution, measurement, quantum circuits), canonical algorithms (quantum kernel methods, variational quantum circuits (VQCs), quantum neural networks (QNNs), QSVMs, quantum generative adversarial networks (QGANs), encoding strategies (angle, amplitude, basis, and Hamiltonian encoding), optimization landscapes (barren plateaus, parameter shift rules, ansatz design), hardware aware implementation on superconducting (IBM, Google), trapped ion (IonQ), and neutral atom (Pasqal) platforms, empirical benchmarks on near term devices for classification, generative modeling, and quantum chemistry, and pathways to fault tolerant quantum machine learning (FTQML) with error correction (surface codes, logical qubits). Researchers critically assess claims of quantum advantage, identify scenarios where QML may outperform classical ML (small data, high-dimensional feature spaces from quantum systems, kernel estimation), and propose concrete evaluation metrics (quantum-classical cross-validation, resource estimation).
Quantum Machine Learning (QML) has a theoretical advantage over classical algorithms for specific synthetic data that is computationally hard. However, it remains unclear whether such theoretical advantages play a meaningful role for realistic classical data, such as natural images. Quantum structural properties induced by unitary operations or entanglement introduce inductive biases that differ from those of classical models, potentially leading to distinct learning behavior on real-world data. In a fully quantum learning pipeline, classical real-world data are first encoded into quantum states via a quantum feature mapping, analogous to a classical feature extractor, and a quantum classifier then classifies the resulting states. Quantum feature mappings generate representations that are difficult to realize classically, while also inducing representation-level biases that do not necessarily match the structure of realistic data. To enable a fair comparison at the classifier level, we focus on the classifier and use classical feature extractors that already provide powerful representations for natural images. By controlling the data scale and supervision strength, we analyze how the unitary structure of quantum classifiers affects generalization, and show that their effectiveness depends strongly on the geometry of the input representations. These results indicate that quantum classifiers benefit from classical features that are aligned with quantum feature spaces. Our analysis shows that kernel alignment identifies representations compatible with quantum feature spaces, providing insights into translating classical models into quantum algorithms.
As the limits of classical machine learning (ML) become increasingly evident—especially in terms of computational scalability and data processing—quantum computing emerges as a promising frontier capable of addressing these challenges. Quantum Machine Learning (QML) represents the intersection of quantum computing and traditional ML, aiming to leverage quantum phenomena such as superposition, entanglement, and quantum parallelism to enhance learning capabilities, accelerate training, and solve complex problems that are intractable for classical algorithms. This paper provides a comprehensive overview of the evolving field of QML, beginning with the theoretical foundations of quantum computing and its synergy with classical machine learning principles. We explore key QML algorithms, including quantum support vector machines (QSVM), variational quantum classifiers (VQC), quantum neural networks (QNN), and hybrid quantum-classical approaches that exemplify the practical integration of both paradigms. We further examine real-world applications of QML across domains such as drug discovery, finance, climate modeling, and optimization, where quantum enhancements have begun to show early but promising results. Despite its theoretical potential, QML faces substantial limitations, including quantum hardware instability, limited qubit scalability, noise sensitivity, and unresolved challenges in quantum data encoding and interpretability. In synthesizing recent advancements and persistent obstacles, this paper highlights the importance of continued interdisciplinary research, algorithmic refinement, and hardware evolution. We also outline future directions that could lead QML from experimental promise to practical utility, including developments in quantum error correction, benchmarking standards, and application-specific quantum architectures
This thesis investigates the interplay between machine learning (ML) and quantum mechanics to advance quantum machine learning (QML) and quantum calculations, addressing computational challenges in quantum machine learning, materials science, and condensed matter physics. The high dimensionality of quantum systems often renders traditional methods computationally intensive. By integrating classical and quantum ML techniques, innovative algorithms are developed to enhance efficiency and accuracy. The first part investigates the design and optimization of quantum circuit architectures for quantum machine learning, with a focus on quantum support vector machines (QSVM). I develop a Bayesian algorithm that adaptively constructs quantum kernels, achieving superior performance over classical kernels in small-data classification tasks. I also establish an isomorphism between quantum circuits and polyatomic molecules, which enables the restriction of the search space for compositional optimization of quantum circuits. Additionally, I introduce a flexible scheme that maps quantum circuits into graph representations compatible with the neutral atom quantum hardware. Using this circuit-graph mapping scheme, I develop a Gaussian process regression model with quantum evolution kernels and a classical graph neural network to interpolate QSVM accuracy on graph-structured data. The second part applies ML to accelerate quantum calculations. I develop a variational algorithm based on eigenvector continuation to compute ground state energies of particle-phonon systems. This algorithm constructs the lowest eigenvalue and eigenvector for extended lattices by solving eigenvalue problems for small, independent lattice segments, with a lower computational cost. This enables the application of variational quantum eigensolvers to particle-phonon interactions in large and disordered lattices, reducing the demands on quantum resources. I also developed Gaussian process models to accelerate Green’s function calculations for electron-phonon systems, achieving high accuracy by extrapolating from restricted Hilbert spaces to larger systems with lower computational cost. Ultimately, this thesis demonstrates that these advancements pave the way for applications, including the design of materials, enhanced drug discovery, and the development of scalable quantum computing technologies, thereby positioning the integration of ML and quantum physics as a promising approach for future scientific breakthroughs.
This thesis investigates the interplay between machine learning (ML) and quantum mechanics to advance quantum machine learning (QML) and quantum calculations, addressing computational challenges in quantum machine learning, materials science, and condensed matter physics. The high dimensionality of quantum systems often renders traditional methods computationally intensive. By integrating classical and quantum ML techniques, innovative algorithms are developed to enhance efficiency and accuracy. The first part investigates the design and optimization of quantum circuit architectures for quantum machine learning, with a focus on quantum support vector machines (QSVM). I develop a Bayesian algorithm that adaptively constructs quantum kernels, achieving superior performance over classical kernels in small-data classification tasks. I also establish an isomorphism between quantum circuits and polyatomic molecules, which enables the restriction of the search space for compositional optimization of quantum circuits. Additionally, I introduce a flexible scheme that maps quantum circuits into graph representations compatible with the neutral atom quantum hardware. Using this circuit-graph mapping scheme, I develop a Gaussian process regression model with quantum evolution kernels and a classical graph neural network to interpolate QSVM accuracy on graph-structured data. The second part applies ML to accelerate quantum calculations. I develop a variational algorithm based on eigenvector continuation to compute ground state energies of particle-phonon systems. This algorithm constructs the lowest eigenvalue and eigenvector for extended lattices by solving eigenvalue problems for small, independent lattice segments, with a lower computational cost. This enables the application of variational quantum eigensolvers to particle-phonon interactions in large and disordered lattices, reducing the demands on quantum resources. I also developed Gaussian process models to accelerate Green’s function calculations for electron-phonon systems, achieving high accuracy by extrapolating from restricted Hilbert spaces to larger systems with lower computational cost. Ultimately, this thesis demonstrates that these advancements pave the way for applications, including the design of materials, enhanced drug discovery, and the development of scalable quantum computing technologies, thereby positioning the integration of ML and quantum physics as a promising approach for future scientific breakthroughs.