Léo Monbroussou | LIP6 - Équipe QI

Quantum Machine Learning for Industrial Applications

Wed, 26 Nov 2025 00:00:00 +0000

Congratulations Dr.Monbroussou !

Abstract

This thesis investigates the development of Quantum Machine Learning (QML) methods for industrial applications, with a focus on bridging the gap between theoretical results and the constraints of current quantum hardware. Classical machine learning has transformed fields such as healthcare, finance, and logistics, yet it now faces several bottlenecks: the exponential growth of data, rising computational costs, concerns about privacy and security, and the massive energy consumption of large-scale models. Quantum computing, originally conceived for simulating physical systems, has emerged as a promising avenue for accelerating certain learning tasks. However, many quantum algorithms require fault-tolerant quantum computers, which remain out of reach. Variational quantum algorithms, better suited to today’s noisy devices, are considered the most realistic candidates, though they still suffer from training difficulties, a lack of theoretical tools to assess their usefulness, and the challenge of guaranteeing that their behavior cannot be efficiently simulated or approximated classically.

The first part of the thesis examines these issues through subspace-preserving quantum circuits, in particular those that preserve the Hamming weight of states. These circuits possess training-friendly properties, yet they are often classically simulable in polynomial time—illustrating the tension between trainability and genuine quantum advantage. This motivates a shift toward algorithms offering only polynomial advantages but equipped with convergence guarantees. Special attention is given to photonic architectures, which naturally preserve particle number and allow for high repetition rates. Their controllability is characterized, and new, albeit suboptimal, schemes are proposed to exploit polynomial-scale advantages that may have concrete industrial value. Building on these insights, the thesis introduces a family of subspace-preserving quantum algorithms that emulate key components of classical learning. These methods combine theoretical guarantees with favorable training behavior, offering a pragmatic pathway toward near-term industrial adoption of quantum learning, even in the absence of exponential speedups.

The second part presents a theoretical framework based on Fourier analysis of variational circuits. This approach jointly addresses expressivity and trainability and enables systematic comparisons between quantum circuits and classical methods. It identifies distinct convergence conditions and clarifies when surrogate models suffice to approximate quantum behavior. These results provide conceptual tools for designing circuits that are resistant to efficient classical simulation and for better understanding the scenarios in which a genuine quantum advantage may emerge.

By combining an analysis of trainability, the design of tailored architectures, and the development of new analytical tools, this thesis delineates the conditions under which quantum learning can achieve real industrial impact. It shows that while exponential advantages remain difficult to obtain with current devices, polynomial gains, particularly in high-throughput photonic architectures, may already offer a competitive edge. The results thus provide a theoretical and algorithmic foundation for designing quantum models that balance expressivity, trainability, and classical hardness, paving the way for concrete industrial applications of QML.

Quantum Machine Learning for Industrial Applications

Wed, 26 Nov 2025 00:00:00 +0000

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.

Toward quantum advantage with photonic state injection

Fri, 11 Jul 2025 00:00:00 +0000

We propose a new scheme for near-term photonic quantum devices that allows us to increase the expressive power of the quantum models beyond what linear optics can do. This scheme relies upon state injection, a measurement-based technique that can produce states that are more controllable, and solve learning tasks that are believed to be intractable classically. We explain how circuits made of linear optical architectures separated by state injections are well-suited for experimental implementation. In addition, we give theoretical results regarding the evolution of the purity of the resulting states, and we discuss how it impacts the distinguishability of the circuit outputs. Finally, we study a computational subroutine of learning algorithms named probability estimation, and we show that the state injection scheme we propose may offer a potential quantum advantage in a regime that can be more easily achieved than state-of-the-art adaptive techniques. Our analysis offers new possibilities for near-term advantage that rely on overcoming fewer experimental difficulties.

Trainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning

Thu, 15 May 2025 00:00:00 +0000

Quantum machine learning (QML) has become a promising area for real world applications of quantum computers, but near-term methods and their scalability are still important research topics. In this context, we analyze the trainability and controllability of specific Hamming weight preserving variational quantum circuits (VQCs). These circuits use qubit gates that preserve subspaces of the Hilbert space, spanned by basis states with fixed Hamming weight k . In this work, we first design and prove the feasibility of new heuristic data loaders, performing quantum amplitude encoding of ( n k ) -dimensional vectors by training an n -qubit quantum circuit. These data loaders are obtained using controllability arguments, by checking the Quantum Fisher Information Matrix (QFIM)’s rank. Second, we provide a theoretical justification for the fact that the rank of the QFIM of any VQC state is almost-everywhere constant, which is of separate interest. Lastly, we analyze the trainability of Hamming weight preserving circuits, and show that the variance of the l 2 cost function gradient is bounded according to the dimension ( n k ) of the subspace. This proves conditions of existence/lack of Barren Plateaus for these circuits, and highlights a setting where a recent conjecture on the link between controllability and trainability of variational quantum circuits does not apply.

Subspace preserving quantum convolutional neural network architectures

Wed, 01 Jan 2025 00:00:00 +0000

Subspace preserving quantum circuits are a class of quantum algorithms that, relying on some symmetries in the computation, can offer theoretical guarantees for their training. Those algorithms have gained extensive interest as they can offer polynomial speed-up and can be used to mimic classical machine learning algorithms. In this work, we propose a novel convolutional neural network architecture model based on Hamming weight preserving quantum circuits. In particular, we introduce convolutional layers, and measurement based pooling layers that preserve the symmetries of the quantum states while realizing non-linearity using gates that are not subspace preserving. Our proposal offers significant polynomial running time advantages over classical deep-learning architecture. We provide an open source simulation library for Hamming weight preserving quantum circuits that can simulate our techniques more efficiently with GPU-oriented libraries. Using this code, we provide examples of architectures that highlight great performances on complex image classification tasks with a limited number of qubits, and with fewer parameters than classical deep-learning architectures.

Subspace Preserving Quantum Convolutional Neural Network Architectures

Sun, 24 Nov 2024 00:00:00 +0000

Towards quantum advantage with photonic state injection

Sun, 24 Nov 2024 00:00:00 +0000

We propose a new scheme for near-term photonic quantum device that allows to increase the expressive power of the quantum models beyond what linear optics can do. This scheme relies upon state injection, a measurement-based technique that can produce states that are more controllable, and solve learning tasks that are not believed to be tackled classically. We explain how circuits made of linear optical architectures separated by state injections are keen for experimental implementation. In addition, we give theoretical results on the evolution of the purity of the resulting states, and we discuss how it impacts the distinguishability of the circuit outputs. Finally, we study a computational subroutines of learning algorithms named probability estimation, and we show the state injection scheme we propose may offer a potential quantum advantage in a regime that can be more easily achieved that state-of-the-art adaptive techniques. Our analysis offers new possibilities for near-term advantage that require to tackle fewer experimental difficulties.

Subspace Preserving Quantum Convolutional Neural Network Architectures

Thu, 03 Oct 2024 00:00:00 +0000

Trainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning

Mon, 02 Oct 2023 00:00:00 +0000

Quantum machine learning has become a promising area for real world applications of quantum computers, but near-term methods and their scalability are still important research topics. In this context, we analyze the trainability and controllability of specific Hamming weight preserving quantum circuits. These circuits use gates that preserve subspaces of the Hilbert space, spanned by basis states with fixed Hamming weight $k$. They are good candidates for mimicking neural networks, by both loading classical data and performing trainable layers. In this work, we first design and prove the feasibility of new heuristic data loaders, performing quantum amplitude encoding of $\binom{n}{k}$-dimensional vectors by training a n-qubit quantum circuit. Then, we analyze more generally the trainability of Hamming weight preserving circuits, and show that the variance of their gradients is bounded according to the size of the preserved subspace. This proves the conditions of existence of Barren Plateaus for these circuits, and highlights a setting where a recent conjecture on the link between controllability and trainability of variational quantum circuits does not apply.