arXiv subjects

Jose Luis Rosales

Publications and source records attributed to Jose Luis Rosales.

6 recordsLinked to original sources

arXiv2026

Quantum-Inspired Hamiltonian Optimization, Stochastic Tensor Networks and Adaptive Congestion Routing for Large-Scale QKD Networks

Quantum Key Distribution (QKD) networks require routing methodologies capable of jointly optimizing latency, secret key generation rate, congestion, finite capacity and operational security constraints under dynamically evolving traffic conditions. In this work we introduce a quantum-inspired optimization framework for adaptive multi-demand routing in QKD communication networks based on effective Hamiltonian modelling, Quantum Monte Carlo inspired annealing and stochastic Tensor-Network State (TNS) compression. The communication network is represented as a stochastic interacting graph whose routing configurations evolve under an effective Hamiltonian containing latency, keyrate, congestion, risk and capacity terms. The resulting optimization landscape is explored through two complementary approaches: a stochastic Metropolis annealer based on incremental local Hamiltonian updates, and a stochastic boundary-MPS tensor-network approximation that compresses the low-energy routing sector through thermal branch selection. The resulting framework establishes a scalable bridge between QKD network orchestration, statistical-physics-inspired optimization, tensor-network compression and future quantum-native routing systems.

quant-ph↗

arXiv2022

Resonant Ion Confinement Fusion Concept

Based on the theorized possibilities of resonant ion confinement, for a Deuteron cloud in a Penning-Malmberg trap with a specially configured rotating wall, the opportunity to design a new type of fusion device is prospected. It is proven that, for some trap configurations, nuclear fusion reactions should take place and, in that case, Lawson's criterion for an efficient fusion reactor is met. Furthermore, the reactor could have a compact design and, since it should not require a large facility, it can function as a fusion cell with a pure ion thermal gas.

physics.gen-ph↗

arXiv2020

Quantum Chaos and the Spectrum of Factoring

There exists a Hamiltonian formulation of the factorisation problem which also needs the definition of a factorisation ensemble (a set to which factorable numbers, $N'=x'y'$, having the same trivial factorisation algorithmic complexity, belong). For the primes therein, a function $E$, that may take only discrete values, should be the analogous of the energy from a confined system of charges in a magnetic trap. This is the quantum factoring simulator hypothesis connecting quantum mechanics with number theory. In this work, we report numerical evidence of the existence of this kind of discrete spectrum from the statistical analysis of the values of $E$ in a sample of random OpenSSL n-bits moduli (which may be taken as a part of the factorisation ensemble). Here, we show that the unfolded distance probability of these $E$'s fits to a {\it Gaussian Unitary Ensemble}, consistently as required, if they actually correspond to the quantum energy levels spacing of a magnetically confined system that exhibits chaos. The confirmation of these predictions bears out the quantum simulator hypothesis and, thereby, it points to the existence of a liaison between quantum mechanics and number theory. Shor's polynomial time complexity of the quantum factorisation problem, from pure quantum simulation primitives, was obtained.

quant-ph↗

arXiv2018

Quantum simulation of the integer factorization problem: Bell states in a Penning trap

The arithmetic problem of factoring an integer $N$ can be translated into the physics of a quantum device, a result that supports Pólya's and Hilbert's conjecture to prove Riemann's hypothesis. The energies of this system, being univocally related to the factors of $N$, are the eigenvalues of a bounded Hamiltonian. Here we solve the quantum conditions and show that the histogram of the discrete energies, provided by the spectrum of the system, should be interpreted in number theory as the relative probability for a prime to be a factor candidate of $N$. This is equivalent to a quantum sieve that is demonstrated to require only $ o(\log \sqrt N)^3$ energy measurements to solve the problem, recovering Shor's complexity result. Hence, the outcome can be seen as a probability map that a pair of primes solve the given factorization problem. Furthermore, we show that a possible embodiment of this quantum simulator corresponds to two entangled particles in a Penning trap. The possibility to build the simulator experimentally is studied in detail. The results show that factoring numbers, many orders of magnitude larger than those computed with experimentally available quantum computers, is achievable using typical parameters in Penning traps.

quant-ph↗

arXiv2016

Quantum Simulation of the Factorization Problem

Feynman's prescription for a quantum simulator was to find a hamitonian for a system that could serve as a computer. Pólya and Hilbert conjecture was to demonstrate Riemann's hypothesis through the spectral decomposition of hermitian operators. Here we study the problem of decomposing a number into its prime factors, $N=xy$, using such a simulator. First, we derive the hamiltonian of the physical system that simulate a new arithmetic function, formulated for the factorization problem, that represents the energy of the computer. This function rests alone on the primes below $\sqrt N$. We exactly solve the spectrum of the quantum system without resorting to any external ad-hoc conditions, also showing that it obtains, for $x\ll \sqrt{N}$, a prediction of the prime counting function that is almost identical to Riemann's $R(x)$ function. It has no counterpart in analytic number theory and its derivation is a consequence of the quantum theory of the simulator alone.

quant-ph↗

arXiv2016

Simulating Factorization with a Quantum Computer

Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum computer would eventually weaken these algorithms. In this paper, one follows Feynman's prescription for a computer to simulate the physics corresponding to the algorithm of factoring a large number $N$ into primes. Using Dirac-Jordan transformation theory one translates factorization into the language of quantum hermitical operators, acting on the vectors of the Hilbert space. This leads to obtaining the ensemble of factorization of $N$ in terms of the Euler function $φ(N)$, that is quantized. On the other hand, considering $N$ as a parameter of the computer, a Quantum Mechanical Prime Counting Function $π_{QM}(x)$, where $x$ factorizes $N$, is derived. This function converges to $π(x)$ when $N\gg x$. It has no counterpart in analytic number theory and its derivation relies on semiclassical quantization alone.

quant-ph↗