arXiv subjects

Said Lantigua

Publications and source records attributed to Said Lantigua.

3 recordsLinked to original sources

arXiv2025

A Classical-Quantum Hybrid Architecture for Physics-Informed Neural Networks

In this work, we introduce the Quantum-Classical Hybrid Physics-Informed Neural Network with Multiplicative and Additive Couplings (QPINN-MAC): a novel hybrid architecture that integrates the framework of Physics-Informed Neural Networks (PINNs) with that of Quantum Neural Networks (QNNs). Specifically, we prove that through strategic couplings between classical and quantum components, the QPINN-MAC retains the universal approximation property, ensuring its theoretical capacity to represent complex solutions of ordinary differential equations (ODEs). Simultaneously, we demonstrate that the hybrid QPINN-MAC architecture actively mitigates the barren plateau problem, regions in parameter space where cost-function gradients decay exponentially with circuit depth, a fundamental obstacle in QNNs that hinders optimization during training. Furthermore, we prove that these couplings prevent gradient collapse, ensuring trainability even in high-dimensional regimes. Thus, our results establish a new pathway for constructing quantum-classical hybrid models with theoretical convergence guarantees, which are essential for the practical application of QPINNs.

quant-ph↗

arXiv2024

Hartman Effect from a Geometrodynamic Extension of Bohmian Mechanics

This paper develops a geometrodynamic extension of Bohmian mechanics to describe quantum tunneling through a potential barrier, treating particle trajectories as geodesics in an Alcubierre-type spacetime. The model provides analytical expressions for the quantum potential, particle dynamics, and tunneling time, explicitly linked to the underlying spacetime geometry. For narrow barriers, the tunneling time depends on the barrier width, while for sufficiently wide barriers, it saturates to a constant value-recovering the Hartman effect. This behavior arises from a geometric self-regulation mechanism, where the quantum potential dynamically adjusts the spacetime distortion to maintain a fixed tunneling time, consistent with relativistic causality despite effective superluminal propagation. The results establish a direct connection between quantum tunneling and spacetime geometry, offering a unified framework to interpret the Hartman effect. This approach naturally incorporates relativistic constraints while suggesting that similar geometric mechanisms may underlie other quantum phenomena, such as topological phases in condensed matter systems.

quant-ph↗

arXiv2023

Influence of spin on tunneling times in the super-relativistic regime

For the relativistic tunneling effect described using Dirac's equation, in [Phys. Rev. A 70, 052112 (2004)] the authors presented the deduction of a general result that allows for the determination of the phase time (group delay) as the sum of the particle dwell time inside a potential barrier and of the self-interference delay associated with the incident and reflected wave functions interaction. In this article, a mathematical model is derived through a construction analogous to the proposal mentioned above, but based on an alternative representation for Dirac's equation. This representation is similar to the one introduced in [Found. Phys. 45, 1586 (2015)]. Thus, from the application of this model in the study of the tunneling effect in the absence of an external magnetic field, the influence of spin on the tunneling times is described. More specifically, the tunneling time is obtained as the sum of the dwell times inside the potential barrier for particles with spin up and spin down and the self-interaction time associated with the incident and reflected wave functions for particles with spin up.

quant-ph↗