arXiv subjects

Ulysse Chabaud

Publications and source records attributed to Ulysse Chabaud.

At least 37 records · Page 2Linked to original sources

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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arXiv2026

Shedding light on classical shadows: learning photonic quantum states

Learning quantum state properties is both a fundamental and practical problem in quantum information theory. Classical shadows have emerged as an efficient method for estimating properties of unknown quantum states, with rigorous statistical guarantees, by performing randomized measurement on few copies of the state. With the advent of photonic technologies, formulating efficient learning algorithms for such platforms comes out as a natural problem. Here, we introduce a practical classical shadow protocol for learning photonic quantum states via randomized passive linear optical transformations and photon-number measurement. We provide rigorous theoretical guarantees showing that our scheme is sample- and time-efficient for measuring physical observables of interest. We experimentally demonstrate our photonic classical shadow protocol on both a twelve-mode and a twenty-four-mode integrated quantum processing unit, and showcase its versatility with five different applications, including Hamiltonian measurement and learning complex photonic states.

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arXiv2026

Universality of Classically Trainable, Quantum-Deployed Boson-Sampling Generative Models

Recent work on the instantaneous quantum polynomial-time (IQP) quantum-circuit Born machine (QCBM) highlights a promising paradigm for generative modeling: train classically, deploy quantumly. In this setting, the training objective can be evaluated efficiently on a classical computer, while sampling from the resulting model may still be classically intractable. Furthermore, in the IQP-QCBM framework, extending the model family with ancillary qubits has been proven to yield universality. This paper asks whether similar results hold for linear-optical generative models. To this end, we introduce the Boson Sampling Born Machine (BSBM). Our analysis retraces analogous steps as were found for IQP-QCBMs with twists. Using recent results that enable classical approximation of broad classes of expectation values in linear optics, we show that BSBMs can be trained classically for wide families of loss functions. Next, we argue that "basic" BSBMs are not universal generative models, and that universality can be achieved by expanding the model while preserving efficient classical training and sampling hardness. In our approach, we introduce and analyze the role of constant-function postprocessing, generalizing the construction for IQP-QCBMs, which under suitable conditions can lead to universality while preserving the hardness of classically simulating the models. We showcase a family of BSBMs, characterized by a single hyperparameter, that allows for a monotonic increase in expressivity toward universality while retaining the capacity to represent ostensibly hard distributions. Furthermore, we discuss the possible modalities for the efficient classical training, in the sense of efficient estimation of gradients of the loss function.

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arXiv2026

Extreme non-negative Wigner functions

Providing an operational characterization of the Wigner-positive states (WPS), i.e., the set of quantum states with non-negative Wigner function, is a longstanding open problem. For pure states, the only WPS are Gaussian states, but the situation is considerably more subtle for mixed states. Here, we approach the problem using convex geometry, reducing the question to the characterization of the extreme points of the set of WPS. We give a constructive method to generate a large class of such extreme WPS, which combines the following steps: (i) we characterize the phase-invariant extreme points of the superset of Wigner-positive quasi-states (WPQS); (ii) we introduce a new quantum map, named Vertigo map, which maps extreme WPQS to extreme WPS while preserving phase invariance; (iii) we identify families of extremality-preserving maps and use them to obtain extreme WPS while relaxing phase invariance. Our construction generates all extreme WPS of low dimension, starting from a specific kind of WPS known as beam-splitter states. Our results build upon new mathematical properties of the set of WPS derived in a companion paper and unveil the remarkable structure of mixed states with non-negative Wigner functions.

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arXiv2026

A unified framework for Bell inequalities from continuous-variable contextuality

Although the original EPR paradox was formulated in terms of position and momentum, most studies of these phenomena have focused on measurement scenarios with only a discrete number of possible measurement outcomes. Here, we present a framework for studying non-locality that is agnostic to the dimension of the physical systems involved, allowing us to probe purely continuous-variable, discrete-variable, or hybrid non-locality. Our approach allows us to find the optimal Bell inequality for any given measurement scenario and quantifies the amount of non-locality that is present in measurement statistics. This formalism unifies the existing literature on continuous-variable non-locality and allows us to identify new states in which Bell non-locality can be probed through homodyne detection. Notably, we find the first example of continuous-variable non-locality that cannot be mapped to a CHSH Bell inequality. Moreover, we provide several examples of simple hybrid DV-CV entangled states that could lead to near-term violation of Bell inequalities.

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arXiv2026

When quantum resources backfire: Non-gaussianity and symplectic coherence in noisy bosonic circuits

Analyzing the impact of noise is of fundamental importance to understand the advantages provided by quantum systems. While the classical simulability of noisy discrete-variable systems is increasingly well understood, noisy bosonic circuits are more challenging to simulate and analyze. Here, we address this gap by introducing the $\textit{displacement propagation}$ algorithm, a continuous-variable analogue of Pauli propagation for simulating noisy bosonic circuits. By exploring the interplay of noise and quantum resources, we identify several computational phase transitions, revealing regimes where even modest noise levels render bosonic circuits efficiently classically simulable. In particular, our analysis reveals a surprising phenomenon: computational resources usually associated with bosonic quantum advantage, namely non-Gaussianity and symplectic coherence, can make the system easier to classically simulate in presence of noise.

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arXiv2026

The stellar decomposition of Gaussian quantum states

We introduce the stellar decomposition, a novel method for characterizing non-Gaussian states produced by photon-counting measurements on Gaussian states. Given an $(m+n)$-mode Gaussian state $G$, we express it as an $(m+n)$-mode "Gaussian core state" $G_{\mathrm{core}}$ followed by an $m$-mode Gaussian transformation $T$ that only acts on the first $m$ modes. The defining property of the Gaussian core state $G_{\mathrm{core}}$ is that measuring the last $n$ of its modes in the photon-number basis leaves the first $m$ modes on a finite Fock support, i.e. a core state. Since $T$ is measurement-independent and $G_{\mathrm{core}}$ has an exact and finite Fock representation, this decomposition exactly describes all non-Gaussian states obtainable by projecting $n$ modes of $G$ onto the Fock basis. For pure states we prove that a physical pair $(G_{\mathrm{core}}, T)$ always exists with $G_{\mathrm{core}}$ pure and $T$ unitary. For mixed states, we establish necessary and sufficient conditions for $(G_{\mathrm{core}}, T)$ to be a Gaussian mixed state and a Gaussian channel. We also develop a semidefinite program to extract the "largest" possible Gaussian channel when these conditions fail. Finally, we present a formal stellar decomposition for generic operators, which is useful in simulations where the only requirement is that the two parts contract back to the original operator. The stellar decomposition leads to practical bounds on achievable state quality in photonic circuits and for GKP state generation in particular. Our results are based on a new characterization of Gaussian completely positive maps in the Bargmann picture, which may be of independent interest.

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arXiv2025

Characterising the sets of quantum states with non-negative Wigner function

For Hilbert spaces $\mathcal H\subseteq L^2(\mathbb R)$ we consider the convex sets $\mathcal D_+(\mathcal H)$ of Wigner-positive states (WPS), i.e.~density matrices over $\mathcal H$ with non-negative Wigner function. We investigate the topological structure of these sets, namely concerning closure, compactness, interior and boundary (in a relative topology induced by the trace norm). We also study their geometric structure and construct minimal sets of states that generate $\mathcal D_+(\mathcal H)$ through convex combinations. If $\mathcal H$ is finite-dimensional, the existence of such sets follows from a central result in convex analysis, namely the Krein-Milman theorem. In the infinite-dimensional case $\mathcal H=L^2(\mathbb R)$ this is not so, due to lack of compactness of the set $\mathcal D_+(\mathcal H)$. Nevertheless, we prove that a Krein-Milman theorem holds in this case, which allows us to extend most of the results concerning the sets of generators to the infinite-dimensional setting. Finally, we study the relation between the finite and infinite-dimensional sets of WPS, and prove that the former provide a hierarchy of closed subsets, which are also proper faces of the latter. These results provide a basis for an operational characterisation of the extreme points of the sets of WPS, which we undertake in a companion paper. Our work offers a unified perspective on the topological and geometric properties of the sets of WPS in finite and infinite dimensions, along with explicit constructions of minimal sets of generators.

math-ph↗

arXiv2025

On the role of coherence for quantum computational advantage

Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness and coherence are arguably of great significance. We introduce path coherence as a measure of the coherent paths interferences arising in a quantum computation. Leveraging the sum-over-paths formalism, we obtain a classical algorithm for estimating quantum transition amplitudes, the complexity of which scales with path coherence. As path coherence relates to the hardness of classical estimation of quantum transition amplitudes, it provides a new perspective on the role of coherence in quantum computational advantage. Beyond their fundamental significance, our results have practical applications for simulating large classes of quantum computations with classical computers.

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arXiv2025

Bounding the computational power of bosonic systems

Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an exponentially greater complexity of state tomography [MMB+24] or a factoring algorithm in constant space [BCCRK24]. Yet, it remains unclear whether this structural difference of bosonic systems may also translate to a practical computational advantage over finite-dimensional quantum computers. Here we take a step towards answering this question by showing that universal bosonic quantum computations can be simulated in polynomial space (and exponential time) on a classical computer, significantly improving the best previous upper bound requiring exponential memory [CJMM24]. In complexity-theoretic terms, we improve the best upper bound on $\textsf{CVBQP}$ from $ \textsf{EXPSPACE}$ to $\textsf{PSPACE}$. This result is achieved using a simulation strategy based on finite energy cutoffs and approximate coherent state decompositions. While we propose ways to potentially refine this bound, we also present arguments supporting the plausibility of an exponential computational advantage of bosonic quantum computers over their discrete-variable counterparts. Furthermore, we emphasize the role of circuit energy as a resource and discuss why it may act as the fundamental bottleneck in realizing this advantage in practical implementations.

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arXiv2025

On the complex zeros of the wavefunction

The Schrödinger wavefunction is ubiquitous in quantum mechanics, quantum chemistry, and bosonic quantum information theory. Its zero-set for fermionic systems is well-studied and central for determining chemical properties, yet for bosonic systems the zero-set is less understood, especially in the context of characterizing non-classicality. Here we study the zeros of such wavefunctions and give them a novel information-theoretic interpretation. Our main technical result is showing that the wavefunction of most bosonic quantum systems can be extended to a holomorphic function over the complex plane, allowing the application of powerful techniques from complex analysis. As a consequence, we prove a version of Hudson's theorem for the wavefunction and characterize Gaussian dynamics as classical motion of the wavefunction zeros. Our findings suggest that the non-Gaussianity of quantum optical states can be detected by measuring a single quadrature of the electromagnetic field, which we demonstrate in a companion paper [arXiv:2507.23005]. More generally, our results show that the non-Gaussian features of bosonic quantum systems are encoded in the zeros of their wavefunction.

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arXiv2025

Complexity of quantum tomography from genuine non-Gaussian entanglement

Quantum state tomography, a fundamental tool for quantum physics, usually requires a number of state copies that scale exponentially with the system size, owing to the intricate quantum correlations between subsystems. We show that, in bosonic systems, the nature of correlations indeed fully determines this scaling. Motivated by the Hong-Ou-Mandel effect and Boson-sampling, we define Gaussian-entanglable (GE) states, produced by generalized interference between separable bosonic modes. GE states greatly extend the Gaussian family, encompassing arbitrary separable states, multi-mode Gottesman-Kitaev-Preskill codes, entangled cat states, and Boson-sampling outputs -- resources for error correction and quantum advantage. Nonetheless, we prove that an m-mode pure GE state is learnable with only poly(m) copies, by providing an explicit protocol involving only heterodyne detection and classical post-processing. For states outside GE, we introduce an operational monotone -- the minimum number of ancillary modes required to render them GE -- and prove that it exactly captures the exponential overhead in tomography. As a by-product, we show that deterministic generation of NOON states with N>=3 photons by two-mode interference is impossible.

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arXiv2025

Observation of Lie algebraic invariants in Quantum Linear Optics

Over the past few years, various methods have been developed to engineeer and to exploit the dynamics of photonic quantum states as they evolve through linear optical networks. Recent theoretical works have shown that the underlying Lie algebraic structure plays a crucial role in the description of linear optical Hamiltonians, as such formalism identifies intrinsic symmetries within photonic systems subject to linear optical dynamics. Here, we experimentally investigate the role of Lie algebra applied to the context of Boson sampling, a pivotal model to the current understanding of computational complexity regimes in photonic quantum information. Performing experiments of increasing complexity, realized within a fully-reconfigurable photonic circuit, we show that sampling experiments do indeed fulfill the constraints implied by a Lie algebraic structure. In addition, we provide a comprehensive picture about how the concept of Lie algebraic invariant can be interpreted from the point of view of n-th order correlation functions in quantum optics. Our work shows how Lie algebraic invariants can be used as a benchmark tool for the correctness of an underlying linear optical dynamics and to verify the reliability of Boson Sampling experiments. This opens new avenues for the use of algebraic-inspired methods as verification tools for photon-based quantum computing protocols.

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arXiv2025

The symplectic rank of non-Gaussian quantum states

Non-Gaussianity is a key resource for achieving quantum advantages in bosonic platforms. Here, we investigate the symplectic rank: a novel non-Gaussianity monotone that satisfies remarkable operational and resource-theoretic properties. Mathematically, the symplectic rank of a pure state is the number of symplectic eigenvalues of the covariance matrix that are strictly larger than the ones of the vacuum. Operationally, it (i) is easy to compute, (ii) emerges as the smallest number of modes onto which all the non-Gaussianity can be compressed via Gaussian unitaries, (iii) lower bounds the non-Gaussian gate complexity of state preparation independently of the gate set, (iv) governs the sample complexity of quantum tomography, and (v) bounds the computational complexity of bosonic circuits. Crucially, the symplectic rank is non-increasing under post-selected Gaussian operations, leading to strictly stronger no-go theorems for Gaussian conversion than those previously known. Remarkably, this allows us to show that the resource theory of non-Gaussianity is irreversible under exact Gaussian operations. Finally, we show that the symplectic rank is a robust non-Gaussian measure, explaining how to witness it in experiments and how to exploit it to meaningfully benchmark different bosonic platforms. In doing so, we derive lower bounds on the trace distance (resp. total variation distance) between arbitrary states (resp. classical probability distributions) in terms of the norm distance between their covariance matrices, which may be of independent interest.

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arXiv2025

Photonic quantum information processing using the frequency continuous-variable of single photons

The celebrated Hong--Ou--Mandel effect illustrates the richness of two-photon interferometry. In this work, we demonstrate that this extends to the realm of time-frequency interferometry. Taking advantage of the mathematical analogy which can be drawn between the frequency and quadrature degrees of freedom of light when there is a single photon in each auxiliary mode, we consider the equivalent of the Hong--Ou--Mandel effect in the frequency domain. In this setting, the $n$-Fock state becomes equivalent to a single-photon state with a spectral wave function given by the $n^{th}$ Hermite--Gauss function and destructive interference corresponds to vanishing probability of detecting single photons with an order one Hermite--Gauss spectral profile. This compelling analogy motivates us to propose an interferometric strategy that uses a frequency-engineered two-photon state to achieve enhanced phase precision that scales inversely with the number of modes. Finally, we generalise the Gaussian Boson Sampling model to time-frequency degrees of freedom of single photons.

quant-ph↗

arXiv2025

Quantum machine learning with Adaptive Boson Sampling via post-selection

The implementation of large-scale universal quantum computation represents a challenging and ambitious task on the road to quantum processing of information. In recent years, an intermediate approach has been pursued to demonstrate quantum computational advantage via non-universal computational models. A relevant example for photonic platforms has been provided by the Boson Sampling paradigm and its variants, which are known to be computationally hard while requiring at the same time only the manipulation of the generated photonic resources via linear optics and detection. Beside quantum computational advantage demonstrations, a promising direction towards possibly useful applications can be found in the field of quantum machine learning, considering the currently almost unexplored intermediate scenario between non-adaptive linear optics and universal photonic quantum computation. Here, we report the experimental implementation of quantum machine learning protocols by adding adaptivity via post-selection to a Boson Sampling platform based on universal programmable photonic circuits fabricated via femtosecond laser writing. Our experimental results demonstrate that Adaptive Boson Sampling is a viable route towards dimension-enhanced quantum machine learning with linear optical devices.

quant-ph↗

arXiv2025

Interplay of resources for universal continuous-variable quantum computing

Quantum resource theories identify the features of quantum computers that provide their computational advantage over classical systems. We investigate the resources driving the complexity of classical simulation in the standard model of continuous-variable quantum computing, and their interplay enabling computational universality. Specifically, we uncover a new property in continuous-variable circuits, analogous to coherence in discrete-variable systems, termed symplectic coherence. Using quadrature propagation across multiple computational paths, we develop an efficient classical simulation algorithm for continuous-variable computations with low symplectic coherence. This establishes symplectic coherence as a necessary resource for universality in continuous-variable quantum computing, alongside non-Gaussianity and entanglement. Via the Gottesman--Kitaev--Preskill encoding, we show that the interplay of these three continuous-variable quantum resources mirrors the discrete-variable relationship between coherence, magic, and entanglement.

quant-ph↗

arXiv2025

Can effective descriptions of bosonic systems be considered complete?

Bosonic statistics give rise to remarkable phenomena, from the Hong-Ou-Mandel effect to Bose-Einstein condensation, with applications spanning fundamental science to quantum technologies. Modeling bosonic systems relies heavily on effective descriptions: typical examples include truncating their infinite-dimensional state space and restricting their dynamics to a simple class of Hamiltonians, such as polynomials of canonical operators, which are used to define quantum computing over bosonic modes. However, many natural bosonic Hamiltonians do not belong to this simple class, and some quantum effects harnessed by bosonic computers inherently require infinite-dimensional spaces, questioning the validity of such effective descriptions of bosonic systems. How can we trust results obtained with such simplifying assumptions to capture real effects? Driven by the increasing importance of bosonic systems for quantum technologies, we solve this outstanding problem by showing that these effective descriptions do in fact capture the relevant physics of bosonic systems. Our technical contribution is twofold: firstly, we prove that any physical, bosonic unitary evolution can be strongly approximated by a finite-dimensional unitary evolution; secondly, we show that any finite-dimensional unitary evolution can be generated exactly by a bosonic Hamiltonian that is a polynomial of canonical operators. Beyond their fundamental significance, our results have implications for classical and quantum simulations of bosonic systems, they provide universal methods for engineering bosonic quantum states and Hamiltonians, they show that polynomial Hamiltonians do generate universal gate sets for quantum computing over bosonic modes, and they lead to an infinite-dimensional Solovay--Kitaev theorem.

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