arXiv subjects

Eliott Z. Mamon

Publications and source records attributed to Eliott Z. Mamon.

5 recordsLinked to original sources

arXiv2026

Orbit dimensions in linear and Gaussian quantum optics

We study the dimension of the manifold of quantum states (called orbit) that a given bosonic state can reach under linear or quadratic Hamiltonian evolutions. That is, we investigate how many directions in the Hilbert space a state can explore in these sub-universal regimes. After showcasing a simple way to compute orbit dimensions, we find that these topological quantities reveal fundamental insights into the structure of attainable state spaces (e.g., boson bunching does not increase the number of accessible directions) with multifaceted consequences. First, we illustrate how they can alone yield no-go results for some transformations. We then propose ways to probe orbit dimensions using homodyne/heterodyne measurements on pure states, or photon counters on two copies of general states. We also relate orbit dimensions to the number of directions accessible to bosonic variational circuits. Next, we study links between orbit dimensions and the resource theory of non-Gaussianity (resp. $P$-nonclassicality), and prove that free states coincide with a unique minimal-dimension orbit in the pure multimode case, under Gaussian (resp. displaced-linear) unitaries. We then extend this result to a mixed-state setting, provided that an alternative convex-roof-based definition of orbit dimensions is taken; however, we show that those fail to be fixed-mode monotones under the respective free operations. Our entire framework is proven to hold in both discrete and continuous-variable settings, and can be used with Fock as well as phase-space representations such as the Wigner or stellar representations. Overall, this work offers a new perspective on the structure of reachable quantum states of light, which can help practitioners understand limitations and sources of expressivity and non-Gaussianity (or $P$-nonclassicality) in bosonic quantum information protocols such as quantum machine learning.

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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

Local controllability of heralded quantum linear optics

Photonic linear optical networks provide a versatile platform for quantum information processing and quantum state engineering. However, the set of states that can be generated using passive linear optics alone is fundamentally constrained by bosonic symmetries. Heralding, based on conditional measurements on auxiliary modes, is a widely used technique to overcome these limitations and effectively enlarge the set of accessible states. Despite the widespread use of heralding, it is often unclear how specific ancillary resources impact the overall reachability of the target space. In this work, we investigate the local controllability of photonic states in linear optical networks by analyzing the rank of the Jacobian of the output state with respect to the underlying unitary circuit, which provides a quantitative measure of the dimension of the accessible tangent space at a given configuration. Our analysis ranges from passive linear optics to heralded linear optics, where auxiliary resources and conditional measurements are included. Within this framework, we quantify how different resources enlarge the locally accessible state space beyond that of passive linear optics and determine the resources required for the Jacobian rank to reach its maximal value, thereby achieving full local controllability. As maximal local rank is a necessary condition for global reachability, our framework offers a systematic tool to assess and compare the accessible state space of measurement-based photonic architectures, and to establish practical criteria for the resources needed in high-dimensional quantum state engineering.

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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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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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