arXiv subjects

Léo Monbroussou

Publications and source records attributed to Léo Monbroussou.

10 recordsLinked to original sources

arXiv2026

Hybrid Quantum Neural Networks: Theory, Implementations, and Applications

Artificial intelligence has been transformed by deep neural networks, yet the search for new learning architectures continues. Quantum machine learning offers one such direction, and hybrid quantum neural networks, which combine classical neural-network components with quantum information processing units, have emerged as a practical framework for near-term quantum technologies. However, the rapid development of the field across diverse architectures, benchmarks and hardware assumptions makes it difficult to assess the utility of various proposals, identify where genuine advantages may arise, and determine how practitioners can use these models. While recent benchmarks caution that such gains have not yet been demonstrated at scale, theoretical work has identified tasks on which quantum models hold provable advantages, and hybrid approaches have delivered promising results on practical problems using deliberately compact quantum components and substantially fewer trainable parameters. Here, we review hybrid quantum neural networks for the machine-learning and quantum-machine-learning communities. We summarize their main theoretical and methodological foundations, survey some of the most promising architectures developed so far, and examine their implementation challenges and reported performance. By consolidating these perspectives, this review provides a structured view of the state of the field and helps identify promising paths for future research and application-driven development.

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arXiv2026

Classical simulation and model concentration in passive linear optics

Passive linear optics is a restricted model of quantum computation, with complexity-theoretic evidence of quantum advantage for sampling tasks and low losses that make it attractive for near-term algorithms. In qubit architectures, a body of work has revealed a close connection between barren plateaus and classical simulability. Whether an analogous tradeoff exists for bosonic systems remains largely unexplored. Building on a recently developed representation-theoretic framework for moments of random passive linear-optical circuits, we characterize the concentration of expectation values for relevant families of particle-number-preserving observables by evaluating their projections into irreducible representations of the unitary group and analyzing their asymptotic scaling. We show that concentration is governed by the misalignment of the projections into irreducible representations of the input state and the observable, giving a unified representation-theoretic interpretation of generalized entanglement and locality in the bosonic setting. We further relate these concentration properties to existing classical simulation techniques, identifying broad classes of trainable observables that admit efficient classical simulation. Conversely, we identify Fock-state inputs and observables that appear to evade exponential concentration while retaining a polynomially large signal component not accessible to known efficient classical simulation methods. The separation is only partial: most of the signal remains classically tractable, and the residual part, while not exponentially suppressed, is small enough that a truncation serves as a classical surrogate with polynomially small error. Our framework nonetheless provides a systematic route for searching for regimes that unambiguously combine the absence of exponential concentration and lies beyond known efficient classical simulation methods.

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arXiv2026

Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchy

Graphs provide a natural language for relational data in chemistry, biology and optimisation. Graph neural networks (GNNs) have driven much of the recent progress in learning from such data through message passing, a single primitive that generalises convolution and attention. Quantum counterparts have been proposed, but with limited connection to message passing and few guarantees on performance or scalability. More broadly, the trainability of variational quantum circuits is a recognised bottleneck for their wide applicability, and pre-training has emerged as one way to address it. Yet for a quantum model to be useful, it must offer expressivity guarantees along with demonstrable scalability. Here we show how a quantum graph neural network can be built to perform message passing, to be permutation equivariant, and to sit at a chosen level of the Weisfeiler-Leman hierarchy, the standard measure of how finely a model can tell graphs apart. We show that, as for classical GNNs, the training can be done first on small graph instances, allowing for a pre-training that can mitigate usual training issues, and its output can be read out at a cost that stays low as the graph grows. We validate the framework in large-scale simulations of up to 56 qubits across three datasets, on synthetic graphs that ordinary message passing cannot separate, on molecular property prediction, and on the travelling salesperson problem. Our framework opens a path for near-term quantum algorithms with theoretical guarantees and practical scalability, bringing the principles of graph learning into quantum circuit design.

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arXiv2026

When Quantum and Classical Models Disagree: Learning Beyond Minimum Norm Least Square

Quantum Machine Learning algorithms based on Variational Quantum Circuits (VQCs) are important candidates for useful application of quantum computing. It is known that a VQC is a linear model in a feature space determined by its architecture. Such models can be compared to classical ones using various sets of tools, and surrogate models designed to classically approximate their results were proposed. At the same time, quantum advantages for learning tasks have been proven in the case of discrete data distributions and cryptography primitives. In this work, we propose a framework to avoid Random Feature approximation techniques. Using previous results, we establish conditions on the weight vectors of the quantum models that are necessary to avoid these dequantization methods. We show that this theory is compatible with previously proven quantum advantages on discrete inputs, and provides examples of advantages for continuous inputs. This separation is connected to large weight vector norm, and we suggest that this can only happen with a high dimensional feature map. Our results demonstrate that it is possible to design quantum models that cannot be classically approximated with good generalization. In addition, we provide a method to verify that the necessary condition is respected for a quantum model. Finally, we discuss how concentration issues must be considered to design such instances. We expect that our work will be a starting point to design near-term quantum models that avoid dequantization methods by ensuring non-classical convergence properties, and to identify existing quantum models that can be classically approximated.

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arXiv2026

Quantum Machine Learning for Industrial Applications

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.

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arXiv2026

Boson sampling beyond the dilute regime: second moments and anti-concentration

Boson sampling is a leading candidate for demonstrating quantum advantage in photonic systems. Despite significant experimental and theoretical progress, a characterization of its output statistics remains incomplete. This is especially true beyond the dilute regime, where photon collisions and bunching become significant. The associated saturated regime, characterized by mode number growing linearly with photon number, or more generally sub-quadratically, is precisely the regime of greatest experimental interest. As a consequence, anti-concentration of the output distribution--a key ingredient in hardness arguments--remains poorly understood in boson sampling. In this work, we leverage representation-theoretic tools to address this gap, obtaining closed-form expressions for second moments of generic particle-number-preserving bosonic observables. We express these quantities in terms of Hilbert-Schmidt norms of projections onto irreducible components of the operator space and show that these projection norms admit compact analytical expressions by exploiting the underlying symmetry structure. Focusing on Fock state output probabilities, we further establish anti-concentration beyond the dilute regime. Together with recent complexity-theoretic results, our findings strengthen hardness guarantees for boson sampling in experimentally interesting settings.

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arXiv2025

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

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 $\binom{n}{k}$-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 $\binom{n}{k}$ 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.

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arXiv2025

Photonic Quantum Convolutional Neural Networks with Adaptive State Injection

Linear optical architectures have been extensively investigated for quantum computing and quantum machine learning applications. Recently, proposals for photonic quantum machine learning have combined linear optics with resource adaptivity, such as adaptive circuit reconfiguration, which promises to enhance expressivity and improve algorithm performances and scalability. Moreover, linear optical platforms preserve some subspaces due to the fixed number of particles during the computation, a property recently exploited to design a novel quantum convolutional neural networks. This last architecture has shown an advantage in terms of running time complexity and of the number of parameters needed with respect to other quantum neural network proposals. In this work, we design and experimentally implement the first photonic quantum convolutional neural network (PQCNN) architecture based on particle-number preserving circuits equipped with state injection, an approach recently proposed to increase the controllability of linear optical circuits. Subsequently, we experimentally validate the PQCNN for a binary image classification on a photonic platform utilizing a semiconductor quantum dot-based single-photon source and programmable integrated photonic interferometers comprising 8 and 12 modes. In order to investigate the scalability of the PQCNN design, we have performed numerical simulations on datasets of different sizes. We highlight the potential utility of a simple adaptive technique for a nonlinear Boson Sampling task, compatible with near-term quantum devices.

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arXiv2024

Towards quantum advantage with photonic state injection

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.

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arXiv2024

Subspace Preserving Quantum Convolutional Neural Network Architectures

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.

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