This thesis explores the development of Quantum Machine Learning (QML) methods aimed at industrial applications, with a focus on bridging the gap between theoretical results and near-term hardware constraints. Classical Machine Learning (ML) has revolutionized industries such as healthcare, finance, and manufacturing, but faces increasing challenges: the exponential growth of data, high computational cost, privacy and security concerns, and the energy consumption of large-scale models. Quantum computing, originally envisioned for simulating quantum systems, has since been proposed as a path to accelerate machine learning tasks, though many algorithms rely on fault-tolerant quantum computers that remain out of reach. Variational Quantum Algorithms (VQAs) have emerged as the most viable candidates for NISQ devices, yet their integration into industry is hindered by difficulties in trainability, in defining reliable measures of expressivity, and in separating quantum models from their classical simulable counterparts. The first part of the thesis investigates these challenges through the study of subspace-preserving quantum circuits, with particular emphasis on Hamming Weight (HW)-preserving architectures. These circuits are shown to offer favorable trainability properties under certain conditions, addressing conjectures on the avoidance of barren plateaus. However, such advantages often coincide with regimes where circuits can be efficiently simulated on classical hardware, underlining the tension between trainability and genuine quantum advantage. To move beyond this limitation, the thesis examines photonic circuits, which naturally preserve particle number and allow high repetition rates. Their controllability is analyzed, and new suboptimal schemes are introduced to exploit polynomial advantages that remain valuable for industrial use cases. Building on these foundations, the work develops a framework for subspace-preserving quantum algorithms that mimic classical ML building blocks while benefiting from favorable scaling and theoretical guarantees. This approach prioritizes pragmatic utility by ensuring that the algorithms remain both trainable and applicable to near-term devices, even when exponential advantages are unattainable. The second part of the thesis introduces a Fourier-based perspective on variational quantum circuits. By interpreting circuit outputs as Fourier models, this framework provides a unified treatment of expressivity and trainability and allows systematic comparisons with classical learning methods. It establishes conditions under which quantum models converge differently from classical ones and clarifies when surrogate models suffice to approximate quantum behavior. These results yield theoretical tools for designing circuits that resist efficient classical simulation and provide guidelines for ensuring meaningful separation between quantum and classical learning regimes. Through this combination of trainability analysis, architectural design, and Fourier-based theoretical tools, the thesis advances the understanding of how QML can deliver industrial utility in the near and medium term. It emphasizes that while exponential quantum advantage may be elusive with current hardware, polynomial improvements—especially in high-throughput settings such as photonics—can already provide competitive benefits. The results contribute to building a theoretical and algorithmic foundation for practical QML, highlighting a pathway where carefully designed quantum models balance expressivity, trainability, and classical hardness to maximize their industrial relevance.
This thesis explores the development of Quantum Machine Learning (QML) methods aimed at industrial applications, with a focus on bridging the gap between theoretical results and near-term hardware constraints. Classical Machine Learning (ML) has revolutionized industries such as healthcare, finance, and manufacturing, but faces increasing challenges: the exponential growth of data, high computational cost, privacy and security concerns, and the energy consumption of large-scale models. Quantum computing, originally envisioned for simulating quantum systems, has since been proposed as a path to accelerate machine learning tasks, though many algorithms rely on fault-tolerant quantum computers that remain out of reach. Variational Quantum Algorithms (VQAs) have emerged as the most viable candidates for NISQ devices, yet their integration into industry is hindered by difficulties in trainability, in defining reliable measures of expressivity, and in separating quantum models from their classical simulable counterparts. The first part of the thesis investigates these challenges through the study of subspace-preserving quantum circuits, with particular emphasis on Hamming Weight (HW)-preserving architectures. These circuits are shown to offer favorable trainability properties under certain conditions, addressing conjectures on the avoidance of barren plateaus. However, such advantages often coincide with regimes where circuits can be efficiently simulated on classical hardware, underlining the tension between trainability and genuine quantum advantage. To move beyond this limitation, the thesis examines photonic circuits, which naturally preserve particle number and allow high repetition rates. Their controllability is analyzed, and new suboptimal schemes are introduced to exploit polynomial advantages that remain valuable for industrial use cases. Building on these foundations, the work develops a framework for subspace-preserving quantum algorithms that mimic classical ML building blocks while benefiting from favorable scaling and theoretical guarantees. This approach prioritizes pragmatic utility by ensuring that the algorithms remain both trainable and applicable to near-term devices, even when exponential advantages are unattainable. The second part of the thesis introduces a Fourier-based perspective on variational quantum circuits. By interpreting circuit outputs as Fourier models, this framework provides a unified treatment of expressivity and trainability and allows systematic comparisons with classical learning methods. It establishes conditions under which quantum models converge differently from classical ones and clarifies when surrogate models suffice to approximate quantum behavior. These results yield theoretical tools for designing circuits that resist efficient classical simulation and provide guidelines for ensuring meaningful separation between quantum and classical learning regimes. Through this combination of trainability analysis, architectural design, and Fourier-based theoretical tools, the thesis advances the understanding of how QML can deliver industrial utility in the near and medium term. It emphasizes that while exponential quantum advantage may be elusive with current hardware, polynomial improvements—especially in high-throughput settings such as photonics—can already provide competitive benefits. The results contribute to building a theoretical and algorithmic foundation for practical QML, highlighting a pathway where carefully designed quantum models balance expressivity, trainability, and classical hardness to maximize their industrial relevance.