This thesis investigates how principles from physics can serve as inductive biases that make learning and optimization more tractable in machine learning and quantum computing. Physical structure - encoded in Hamiltonians, physics-inspired dynamics, circuit architectures, and measurement protocols - constrains the hypothesis class, enabling learning under limited computational and data budgets in high-dimensional settings. The thesis presents four case studies showing how these physics-inspired inductive biases can be incorporated into both classical and quantum models. First, quantum diffusion models are introduced as generative models for quantum states. A Markovian noising process, motivated by statistical physics, defines the forward dynamics, while parameterized quantum circuits implement the reverse dynamics. Second, a Potts-model Hamiltonian is used to formulate a graph-coloring objective, leading to a physics-informed neural architecture that generalizes beyond the training distribution. Third, parameterized quantum circuits and hybrid classical-quantum models are evaluated for an anomaly detection task in highly imbalanced classical transaction data, using circuit structure as an additional inductive bias. Fourth, a data-driven classical-shadow method is developed, in which a neural network maps shadow snapshots to observable expectation values. This work fits into the broader effort of quantum device certification. Overall, the results show that physics-inspired inductive biases are a robust lever for resource-efficient learning, while NISQ-era quantum resources provide modest task- and metric-dependent benefits rather than a consistent advantage over classical baselines.
This thesis investigates how principles from physics can serve as inductive biases that make learning and optimization more tractable in machine learning and quantum computing. Physical structure - encoded in Hamiltonians, physics-inspired dynamics, circuit architectures, and measurement protocols - constrains the hypothesis class, enabling learning under limited computational and data budgets in high-dimensional settings. The thesis presents four case studies showing how these physics-inspired inductive biases can be incorporated into both classical and quantum models. First, quantum diffusion models are introduced as generative models for quantum states. A Markovian noising process, motivated by statistical physics, defines the forward dynamics, while parameterized quantum circuits implement the reverse dynamics. Second, a Potts-model Hamiltonian is used to formulate a graph-coloring objective, leading to a physics-informed neural architecture that generalizes beyond the training distribution. Third, parameterized quantum circuits and hybrid classical-quantum models are evaluated for an anomaly detection task in highly imbalanced classical transaction data, using circuit structure as an additional inductive bias. Fourth, a data-driven classical-shadow method is developed, in which a neural network maps shadow snapshots to observable expectation values. This work fits into the broader effort of quantum device certification. Overall, the results show that physics-inspired inductive biases are a robust lever for resource-efficient learning, while NISQ-era quantum resources provide modest task- and metric-dependent benefits rather than a consistent advantage over classical baselines.
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.
This thesis presents original contributions at the intersection of quantum computing and machine learning, investigating how these two fields can benefit from each other. The first part of the thesis presents two applications of machine learning techniques in quantum computing. The first contribution involves the use of artificial neural networks for the decoding of quantum error correction codes, resulting in faster decoding times while maintaining a high level of accuracy. The originality of this work lies in the application of explainable machine learning techniques to both improve the decoding performance and to provide insights into the decoding process. The second contribution introduces a novel technique based on reinforcement learning to characterize and simulate the noise affecting a quantum chip. This technique reduces the heuristic assumption on the noise model, making it more adaptable to the specific noise characteristics of the quantum device. In the second part of the thesis, we demonstrate, with two examples, how it is possible to implement machine learning algorithms on quantum devices by replacing artificial neural networks with parametrized quantum circuits. The first contribution in this section introduces a quantum anomaly detection algorithm, applied to the field of high-energy physics. This algorithm allows for the identification of anomalous patterns in quantum data, maintaining a level of accuracy comparable to classical algorithms. The novelty of this work lies in the first use of quantum circuits for the task of anomaly detection in a muon drift chamber trigger system, with possible future applications to quantum detector systems in high-energy physics experiments. The second contribution presents the quantum version of a generative diffusion model, able to sample quantum states from a well-defined distribution. This first implementation of a quantum diffusion model is not meant to outperform classical models, but rather to show potential advantages and limitations of these kinds of algorithms. The aim of the thesis is to show how quantum computing can benefit from machine learning, and how machine learning can be implemented on quantum devices, setting the stage for future advancements in both fields.
Quantum machine learning models based on parametrized quantum circuits, also called quantum neural networks (QNNs), are considered to be among the most promising candidates for applications on near-term quantum devices. Here we explore the expressivity and inductive bias of QNNs by exploiting an exact mapping from QNNs with inputs x to classical perceptrons acting on x⊗x (generalised to complex inputs). The simplicity of the perceptron architecture allows us to provide clear examples of the shortcomings of current QNN models, and the many barriers they face to becoming useful general-purpose learning algorithms. For example, a QNN with amplitude encoding cannot express the Boolean parity function for n≥3, which is but one of an exponential number of data structures that such a QNN is unable to express. Mapping a QNN to a classical perceptron simplifies training, allowing us to systematically study the inductive biases of other, more expressive embeddings on Boolean data. Several popular embeddings primarily produce an inductive bias towards functions with low class balance, reducing their generalisation performance compared to deep neural network architectures which exhibit much richer inductive biases. We explore two alternate strategies that move beyond standard QNNs. In the first, we use a QNN to help generate a classical DNN-inspired kernel. In the second we draw an analogy to the hierarchical structure of deep neural networks and construct a layered non-linear QNN that is provably fully expressive on Boolean data, while also exhibiting a richer inductive bias than simple QNNs. Finally, we discuss characteristics of the QNN literature that may obscure how hard it is to achieve quantum advantage over deep learning algorithms on classical data.
Generative Artificial Intelligence is one of the most relevant technologies of our century, enabling digital machines not only to analyze or classify data but also to generate new content such as images, text, and video. This technology relies on deep learning algorithms designed to capture complex relationships from finite data sets. In this context, Diffusion Models have recently emerged as state-of-the-art in deep generative modeling thanks to their ability to produce high-quality data. Their pipeline typically consists of a forward diffusion process, where data samples are progressively corrupted into pure (classical) noise, and a reverse denoising process, where deep neural networks learn to reverse the diffusion process and then generate new synthetic samples. In parallel, Quantum Machine Learning represents one of the most promising applications of quantum computing. However, currently available quantum processors, known as Noisy Intermediate-Scale Quantum (NISQ) devices, are composed of tens or hundreds of noisy qubits. Therefore, designing scalable and efficient practical quantum algorithms represents a significant challenge. This thesis proposes the first generalization of classical Denoising Diffusion Probabilistic Models to the quantum domain, introducing the novel generative paradigm of Quantum Diffusion Models. In particular, the three possible scenarios are formalized and implemented: (i) classical data corrupted with Gaussian noise and a reverse process implemented via a quantum neural network; (ii) quantum data corrupted with quantum noise and a denoising process through a classical deep neural network; and (iii) a fully quantum approach, where both forward and backward processes are implemented within a quantum framework. Subsequently, the impact of different stochastic dynamics in the forward process is analyzed using the formalism of Quantum Stochastic Walks. We observe that a specific hybrid quantum-classical dynamics produces more statistically robust models, capable of generating sets of images closely resembling real ones compared to purely classical dynamics. Furthermore, we propose a hybrid quantum-classical diffusion model based on Quantum Walks that exploits the intrinsic noise of real quantum processors as a useful resource for generating images. This model is implementable on current NISQ devices and scalable, as it allows the generation of images of any size, requiring q + 1 qubits for grayscale images with pixel intensities in the range [0, 2^q - 1]. Finally, an application in the context of medical imaging is presented, specifically the generation of 64 × 64 color images of blood cells from the BloodMNIST dataset and 200 × 200 brain MRI images from the BraTS2020 dataset.
In recent years, quantum computing, as a potential way to break the bottleneck of Moore's Law, has gradually shown its unique advantages in the field of machine learning. Not only can it bring exponential or polynomial acceleration in some specific tasks, it also provides entirely new ways of representing and processing information. Focusing on the core theme of application and method innovation of quantum machine learning in structured data, this thesis systematically studies the theoretical models and practical applications of quantum computing in many sub-fields such as agricultural remote sensing, graph neural networks, and hyperdimensional computing, and explores the adaptability, scalability, and effectiveness of quantum models in real-world tasks. Firstly, in the cropland classification and yield prediction task, this study identifies that traditional neural networks tend to underperform when facing imbalanced and small-sample remote sensing data, often misclassifying minority crop types. To address this, we propose a quantum-classical hybrid recognition framework that integrates quantum feature mapping with classical neural networks. After incorporating quantum feature encoding, we observe a significant improvement in classification performance, especially in cases involving subtle field boundaries and heterogeneous textures. The quantum-enhanced model demonstrates superior accuracy, robustness, and generalization compared to its classical counterpart, validating the advantage of leveraging quantum representations in real-world agricultural datasets. The second part focuses on the learning of graph structure data and proposes to embed the Continuous Time Quantum Walk (CTQW) into the Graph Neural Network (GNN) architecture. This method not only preserves the global interference characteristic of quantum states but also realizes the efficient modeling of graph topology through the spectral graph methods. Experiments show that the proposed method is superior to many classical graph learning models in tasks such as node classification and graph structure inference. The third and fourth components of this thesis collectively explore quantum approaches to hyperdimensional computing (HDC), establishing a progressive transition from native quantum-state-based implementation to quantum-enhanced HDC strategies. Initially, we investigate the intrinsic mathematical correspondence between quantum states and high-dimensional hypervectors, and propose a novel quantum-state-based high-dimensional encoding method. This method is realized through quantum circuits capable of generating hypervectors with controllable entropy, thereby implementing essential HDC operations, such as classification and memory reconstruction, on real quantum hardware. This marks the first successful migration of core HDC mechanisms into a fully quantum-native framework. Building upon this foundation, we further propose the first quantum-enhanced HDC strategy, which does not rely solely on quantum-native implementations but rather utilizes key quantum features to boost the efficiency and expressivity of conventional HDC systems. Specifically, we introduce mechanisms such as quantum-reference-state-based binding, using density matrices to represent superclass states, and quantum state tomography for robust feature extraction. These innovations significantly enhance the resilience and performance of HDC under high-noise and high-dimensional sensing environments. The resulting models achieve superior accuracy and robustness across a variety of multi-class classification tasks, demonstrating the practical benefits of integrating quantum computation into the broader HDC paradigm. In this thesis, experimental validation is carried out in multiple real and simulation environments, including Qiskit and Paddle Quantum platforms, and a complete closed loop was achieved from theoretical derivation, quantum circuit design to end-to-end experimental evaluation. The results show that quantum methods can expand the expressive power of classical models and become an important tool to deal with large-scale, structured data problems in the future. The work in this thesis provides methodological support for quantum machine learning from theory to application, and also expands the research boundaries of high-dimensional computation and graph learning in the quantum background.
Quantum Neural Networks (QNNs) represent a compelling convergence of quantum mechanics and machine learning, yet their practical deployment remains constrained by noise, limited qubit counts, and the cost of full quantum execution. Hybrid quantum-classical (HQC) training offers a pragmatic path forward: parameterized quantum circuits (PQCs) process information in exponentially large Hilbert spaces while classical optimizers update parameters via gradient methods accessible on today's hardware. We present a modular HQC training framework, formalising the parameter-shift rule for hardware-compatible gradient estimation, characterising the barren-plateau phenomenon through a variance-decay analysis, and introducing noise-aware training strategies for NISQ devices. Empirical results from state-vector and shot-based simulation confirm measurable quantum advantage on quantum-structured tasks, with the phase classification benchmark improving +12.1% over a classical MLP baseline. The accompanying open-source library provides a clean abstraction between quantum simulation and classical optimisation, serving as a foundation for near-term quantum machine learning research.