Eliott Mamon | LIP6 - Équipe QI

Eliott Mamon - Orbit dimensions in linear and Gaussian quantum optics

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

Orbit dimensions in linear and Gaussian quantum optics

Ce séminaire, donné par Eliott Mamon, aura lieu le 01 October 2025, à 12:0. Il aura lieu en salle 25-26/105.

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Résumé

In sub-universal quantum platforms such as linear or Gaussian quantum optics, quantum states can behave as different resources, in regard to the extent of their accessible state space (called their orbit) under the action of the restricted unitary group. We propose to study the dimension of a quantum state’s orbit (as a manifold in the Hilbert space), a simple yet nontrivial topological property that can quantify how many states it can reach. As natural invariants under the group, these structural properties of orbits alone can also reveal fundamental impossibilities of enacting certain unitary transformations deterministically. We showcase a general and straightforward way to compute orbit dimensions (for states of finite support in the Fock basis) by leveraging the group’s Lie algebra, and we study their genericity and robustness properties. We also propose approaches to efficiently evaluate orbit dimensions experimentally, using homodyne or heterodyne measurements for pure states or photon counters for general states. Besides, we highlight that the orbit dimension under the Gaussian unitary group serves a non-Gaussianity witness, which we expect to be universal for multimode pure states. While proven in the discrete variable setting (i.e. passive linear optics with an energy cutoff), the validity of our work in the continuous variable setting does rest on a technical conjecture which we do not prove. This talk is based on the following preprint: https://arxiv.org/abs/2506.07995v2

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.