arXiv subjects

Romain Kukla

Publications and source records attributed to Romain Kukla.

3 recordsLinked to original sources

arXiv2025

On multipolar magnetic anomaly detection: multipolar signal subspaces, an analytical orthonormal basis, multipolar truncature and detection performance

In this paper, we consider the magnetic anomaly detection problem which aims to find hidden ferromagnetic masses by estimating the weak perturbation they induce on local Earth's magnetic field. We consider classical detection schemes that rely on signals recorded on a moving sensor, and modeling of the source as a function of unknown parameters. As the usual spherical harmonic decomposition of the anomaly has to be truncated in practice, we study the signal vector subspaces induced by each multipole of the decomposition, proving they are not in direct sum, and discussing the impact it has on the choice of the truncation order. Further, to ease the detection strategy based on generalized likelihood ratio test, we rely on orthogonal polynomials theory to derive an analytical set of orthonormal functions (multipolar orthonormal basis functions) that spans the space of the noise-free measured signal. Finally, based on the subspace structure of the multipole vector spaces, we study the impact of the truncation order on the detection performance, beyond the issue of potential surparametrization, and the behaviour of the information criteria used to choose this order.

eess.SP↗

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.

quant-ph↗

arXiv2024

Type-II Seesaw Higgs triplet productions and decays at the LHC

The Type-II Seesaw Model provides an attractive scenario to account for Majorana-neutrino masses. Its extended Higgs sector, if sufficiently light, can have a rich and distinctive phenomenology at the LHC while yielding automatically an essentially Standard-Model-Higgs-like state. Several phenomenological studies have been devoted to the scalar sector of this model, as well as experimental searches focusing mostly on the (doubly-)charged states. In this paper we present an exhaustive study of the main production and decay channels of all the non-standard scalar states originating from the $SU(2)_L$ doublet and a complex triplet of the model. We stick to scenarios where lepton-number-violating decays are suppressed, for which present experimental limits are still weak, highlighting theoretical parameter sensitivities that were not previously emphasized in the literature and the uncertainties they can induce for the experimental searches at the LHC. A comprehensive classification of the various cascade decays and corresponding Standard Model particle multiplicities is provided. As an illustration, a detailed prospective search study at the LHC with an ATLAS-like detector is carried out on some benchmark points, for charged, doubly-charged, and, for the first time, neutral state productions

hep-ph↗