arXiv subjects

Jesús Fuentes

Publications and source records attributed to Jesús Fuentes.

7 recordsLinked to original sources

arXiv2024

Quantum Machine Learning With Canonical Variables

Utilising dynamic electromagnetic field control over charged particles serves as the basis for a quantum machine learning platform that operates on observables rather than directly on states. Such a platform can be physically realised in ion traps or particle confinement devices that utilise electromagnetic fields as the source of control. The electromagnetic field acts as the ansatz within the learning algorithm. The models discussed are exactly solvable, with exact solutions serving as precursors for learning tasks to emerge, including regression and classification algorithms as particular cases. This approach is considered in terms of canonical variables with semi-classical behaviour, disregarding relativistic degrees of freedom.

quant-ph↗

arXiv2024

Conceptual Problems in Quantum Squeezing

In studies of quantum squeezing, the emphasis is typically placed more on specific squeezed states and their evolution rather than on the dynamical operations that could simultaneously squeeze a broader range of quantum states, regardless of their initial configuration. We explore new developments in this area, facilitated by gently acting external fields which might induce squeezing of the canonical observables $q$ and $p$ in charged particles. The extensive research in this field has yielded many valuable insights, raising the question of whether there is still room for significant new contributions to our understanding. Nonetheless, we present some exactly solvable instances of this problem, observed in symmetric evolution intervals. These intervals allow for the explicit determination of the temporal dependence of external fields necessary to generate the required evolution operators. Our findings are linked with a straightforward application of Toeplitz matrices, offering a more accessible description of the problem compared to the frequently employed Ermakov-Milne invariants.

quant-ph↗

arXiv2023

Quantum Fuzzy Orbits

This manuscript surveys quantum operations under the influence of harmonic magnetic fields subject to time variations. The author scrutinises the dynamic interplay of these fields and canonical variables, leading to effects such as squeezing, looping effects, and parametric resonances. The time evolution of observables tethered to a time-dependent quadratic Hamiltonian is examined. The results of this inquiry offer contributions to the quantum control theory.

quant-ph↗

arXiv2021

On how generalised entropies without parameters impact information optimisation processes

As an application of generalised statistical mechanics, it is studied a possible route toward a consistent generalised information theory in terms of a family of non-extensive, non-parametric entropies $H^\pm_D(P)$. Unlike other proposals based on non-extensive entropies with a parameter dependence, our scheme is asymptotically equivalent to the one formulated by Shannon, while it differs in regions where the density of states is reasonably small, which leads to information distributions constrained to their background. Two basic concepts are discussed to this aim. First, we prove two effective coding theorems for the entropies $H^\pm_D(P)$. Then we calculate the channel capacity of a binary symmetric channel (BSC) and a binary erasure channel (BEC) in terms of these entropies. We found that processes such as data compression and channel capacity maximisation can be improved in regions where there is a low density of states, whereas for high densities our results coincide with Shannon's formulation.

cs.IT↗

arXiv2021

A superstatistical formulation of complexity measures

It is discussed how the superstatistical formulation of effective Boltzmann factors can be related to the concept of Kolmogorov complexity, generating an infinite set of complexity measures (CMs) for quantifying information. At this level, the information is treated according to its background, which means that the CM depends on the inherent attributes of the information scenario. While the basic Boltzmann factor directly produces the standard complexity measure (SCM), it succeeds in the description of large-scale scenarios where the data components are not interrelated with themselves, thus adopting the behaviour of a gas. What happens in scenarios in which the presence of sources and sinks of information cannot be neglected, needs of a CM other than the one produced by the ordinary Boltzmann factor. We introduce a set of flexible CMs, without free parameters, that converge asymptotically to the Kolmogorov complexity, but also quantify the information in scenarios with a reasonable small density of states. We prove that these CMs are obtained from a generalised relative entropy and we suggest why such measures are the only compatible generalisations of the SCM.

cs.CC↗

arXiv2017

Squeezed Fourier Meets Toeplitz Algebras

We look for new steps on the dynamical operations that may squeeze simultaneously some families of quantum states, independently of their initial shape, induced by softly acting external fields which might produce the squeezing of the canonical observables $q,p$ of charged particles. Also, we present some exactly solvable cases of the problem which appear in the symmetric evolution intervals permitting to find explicitly the time dependence of the external fields needed to generate the required evolution operators. Curiously, our results are interrelated with a simple, non--trivial, anti--commuting algebra of Toeplitz which describes the problem more easily than the frequently used Ermakov--Milne invariants.

quant-ph↗

arXiv2017

Pseudo Spectral Transform for Schrödinger--Poisson Equations

Here we present exact, stationary, parametric solutions to the Schrödinger--Poisson system. We confront two images: on one hand, we draw on the homotopy analysis method which leads us to a nonlinear integral scheme. Indeed, this approach might be simplified by looking for sufficiently smooth solutions vanishing asymptotically. However, since our system possesses stiffness an additional analysis has to be considered. On the other hand, we seek for exact solutions over the inverse scattering method by introducing a pseudo spectral transform. In fact, this pseudo spectral method generalises Korteweg--de Vries family's kernel and let us to circumvent some technical difficulties originally arisen in our first approach although, again, we come to an integral representation, which we test for convergence.

quant-ph↗