arXiv subjects

J. Montes

Publications and source records attributed to J. Montes.

13 recordsLinked to original sources

arXiv2026

Taking Advantage of Noise in Distributed Random Quantum Circuits

Adding noise can make a random quantum circuit look faster without making its unitary dynamics more random. This distinction is especially relevant in modular processors, where local gates randomize each core and scarce inter-core communication must spread that randomness across the full device. In this paper, we study this problem with a reduced second-moment transfer-matrix theory for Pauli second moments in distributed random circuits affected by the amplitude-damping, depolarizing, and dephasing noise channels. The key step is to resolve the noisy spectrum into two branches: a radial branch, describing dissipative loss of non-identity Pauli weight, and an angular branch, describing Haar-like mixing within the surviving nontrivial sector. This separation gives a simple weak-noise criterion: noise is useful for angular randomization only when it suppresses the longitudinal Bloch component more strongly than the transverse plane. Among the three channels considered, this selects amplitude damping as the only locally favorable case, while depolarizing noise is neutral and dephasing is dominated by radial loss. For multicore architectures, we derive a universal first-order law for radial leakage and track the angular branch numerically across different channels, topologies, and core partitions. The results reveal narrow windows of genuine noise-assisted Haar mixing, most clearly for amplitude damping, but rule out a generic speed-up by noise. The framework therefore distinguishes useful noisy randomization from mere dissipation.

quant-ph↗

arXiv2026

Unveiling Semiclassical Structures in Quantum Chaotic Eigenstates Using Neural Networks

Physics-informed neural networks and neural quantum states have consolidated a new paradigm to analyze and discover physical phenomena through constrained neural parametrizations. In this context, we investigate whether the semiclassical structure of the eigenfunctions of a quantum chaotic system can be unveiled through unsupervised learning. To this end, we train a "quantum dictionary", formulated as an overcomplete autoencoder, that sparsely represents the eigenstates of the system, using as an illustration the quantum baker map. The only explicit physical information imposed on the dictionary atoms is their localization in phase space, without providing any kind of information about the periodic orbits of the corresponding classical system. The model achieves high fidelity in reconstructing eigenstates not used during training. By comparing the learned atoms with an independently constructed "semiclassical dictionary", we find that they spontaneously localize on the periodic orbits and develop scar-like structures. This result is interesting in two ways: a localization constraint is sufficient to recover nontrivial semiclassical organization from spectral data and at the same time periodic orbits confirm their fundamental role in the structure of quantum chaotic eigenfunctions. More generally, our proposed architecture opens a new route to learning representations whose atoms optimize other chosen physical properties.

quant-ph↗

arXiv2026

On the question of noise as a resource in quantum computing

Noise is usually regarded as the main obstacle to achieving a scalable quantum advantage, but recent evidence in quantum reservoir computing [L. Domingo, F. Borondo, and G. G. Carlo. Taking advantage of noise in quantum reservoir computing, Scientific Reports, 13:8790, 2023] suggests that certain channels can, in appropriate regimes, improve performance by enriching the reservoir's effective dynamics. Motivated by this idea we propose a geometric mechanism to explain how non-unital noise applied together with a universal gate set leads to a faster approach to Haar-like distributions of the final states. We find that noise of this kind induces an effective volume expansion on the manifold of pure states. In order to intuitively understand this we use a minimal 1 qubit model where we take the amplitude damping channel and combine it with a renormalization rule that associates to each resulting mixed state a representative pure state. This composition defines a globally expanding nonlinear map on the space of pure states. We analytically derive the local area expansion factor and identify the global expansion threshold. Finally, we combine amplitude damping with the G3 = {H, T, CNOT} universal gate set to show how the approach to Haar-like behavior is faster in an appropriate parameter region. This leads us to propose noise as a possible resource in future quantum algorithms.

quant-ph↗

arXiv2025

Universal Configuration for Optimizing Complexity in Variational Distributed Quantum Circuits

Distributed quantum computing represents at present one of the most promising approaches to scaling quantum processors. Current implementations typically partition circuits into multiple cores, each composed of several qubits, with inter-core connectivity playing a central role in ensuring scalability. Identifying the optimal configuration -- defined as the arrangement that maximizes circuit complexity with minimal depth -- thus constitutes a fundamental design challenge. In this work, we demonstrate, both analytically and numerically, the existence of a universal optimal configuration for distributing single and two qubit gates across arbitrary intercore communication topologies in variational distributed circuits. Our proof is based on a complexity measure based on Markov matrices, which quantifies the convergence rate toward the Haar measure, as introduced by Weinstein et al. Finally, we validate our predictions through numerical comparisons with the well established majorization criterion proposed in Ref 2.

quant-ph↗

arXiv2025

Optimal multicore quantum computing with few interconnects

Noisy intermediate-scale quantum processors have produced a quantum computation revolution in recent times. However, to make further advances new strategies to overcome the error rate growth are needed. One possible way out is dividing these devices into many cores. On the other hand, the majorization criterion efficiently classifies quantum circuits in terms of their complexity, which can be directly related to their ability of performing non classically simulatable computations. In this paper, we use this criterion to study the complexity behavior of a paradigmatic universal family of random circuits distributed into several cores with different architectures. We find that the optimal complexity is reached with few interconnects, this giving further hope to actual implementations in nowadays available devices. A universal behavior is found irrespective of the architecture and (approximately) of the core size. We also analyze the complexity properties when scaling processors up by means of adding cores of the same size. We provide a conjecture to explain the results.

quant-ph↗

arXiv2024

Using Lagrangian descriptors to calculate the Maslov index of periodic orbits

The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of non-integrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically demanding. In this paper, we describe a straightforward technique, for systems with two degrees of freedom, based on the Lagrangian descriptors. Our method is illustrated by applying it to the two-dimensional coupled quartic oscillator.

nlin.CD↗

arXiv2024

Exploring quantum localization with machine learning

We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization. Our approach integrates a versatile quantum phase space parametrization leading to a custom 'quantum' NN, with the pattern recognition capabilities of a modified convolutional model. This design accepts wave functions of any dimension as inputs and makes accurate predictions at an affordable computational cost. This scalability becomes crucial to explore the localization rate at the semiclassical limit, a long standing question in the quantum scattering field. Moreover, the physical meaning built in the model allows for the interpretation of the learning process

quant-ph↗

arXiv2024

Order-chaos transition in correlation diagrams and quantization of period orbits

Eigenlevel correlation diagrams has proven to be a very useful tool to understand eigenstate characteristics of classically chaotic systems. In particular, we showed in a previous publication [Phys. Rev. Lett. 80, 944 (1998)] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing Planck constant, we induced a transition from order to chaos, in which scarred wavefunctions appeared as the interaction of pairs of eigenstates in broad avoided crossings, forming a well defined frontier in the correlation diagram. In this paper, we demonstrate that this frontier can be obtained by means of the semiclassical quantization of the involved scarring periodic orbits. Additionally, in order to calculate the Maslov index of each scarring periodic orbit, which is necessary for the semiclassical quantization procedure, we introduce a novel straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.

nlin.CD↗

arXiv2023

Average localization of resonances on the quantum repeller

There has been a very recent surge in the interest on the localization properties of resonances associated to partially open (scattering) systems, which are of great relevance when studying resonant cavities such as those used in microlasers. Very recently, it has been found that no localization is present in a scaled form of these states. Moreover, a new kind of scarring on structures different from periodic orbits is described for non scaled resonances. In this paper, we analyze the localization of a distribution function corresponding to the quantum LR representation -- based on the non unitary evolution operator decomposition into left and right resonances -- for the partially open quantum tribaker map, a paradigmatic system. We find localization on the shortest periodic orbits. Also, scaled states present enhancements that could not be associated to periodic orbits and that become more evident when looking at the LR representation. These findings open the door for new perspectives on recent theoretical developments.

quant-ph↗

arXiv2021

Lagrangian descriptors for the Bunimovich stadium billiard

We apply the concept of Lagrangian descriptors to the dynamics on the Bunimovich stadium billiard, a 2D ergodic system with singular families of trajectories, namely, the bouncing ball and the whispering gallery orbits. They play a central role in structuring the phase space, which is unveiled here by means of the Lagrangian descriptors applied to the associated map on the boundary. More interestingly, we also consider the open stadium, which in the optical case (Fresnel's laws) can be directly related to recent microlaser experiments. We find that the structure of the emission profile of these systems can be easily described thanks to the open version of the Lagrangian descriptors.

nlin.CD↗

arXiv2015

Equation of state and critical point behavior of hard-core double-Yukawa fluids

A theoretical study on the equation of state and the critical point behavior of hard-core double-Yukawa fluids is presented. Thermodynamic perturbation theory, restricted to first order in the inverse temperature and having the hard-sphere fluid as the reference system, is used to derive a relatively simple analytical equation of state of hard-core multi-Yukawa fluids. Using such an equation of state, the compressibility factor and phase behavior of six representative hard-core double-Yukawa fluids is examined and compared with available simulation results. The effect of varying the parameters of the hard-core double-Yukawa intermolecular potential on the location of the critical point is also analyzed using different perspectives. The relevance of this analysis for fluids whose molecules interact with realistic potentials is also pointed out.

cond-mat.stat-mech↗

arXiv2012

Higher Newton polygons and integral bases

Let $A$ be a Dedekind domain, $K$ the fraction field, $\p$ a non-zero prime ideal of $A$, and $K_\pp$ the completion of $K$ with respect to the $\p$-adic topology. At the input of a monic irreducible separable polynomial, $f(x)\in A[x]$, Montes algorithm determines the factorization of $f(x)$ over $K_\pp[x]$, and it provides essential arithmetic information about the finite extensions of $K_\pp$ determined by the different irreducible factors. In particular, it can be used to compute $\p$-integral bases of the extension of $K$ determined by $f(x)$ \cite{newapp}. In this paper we present new (and faster) methods to compute $\p$-integral bases, based on the use of the quotients of certain divisions with remainder of $f(x)$ that occur along the flow of Montes algorithm.

math.NT↗

arXiv2010

Arithmetic in big number fields: the '+Ideals' package

We introduce our package '+Ideals' for Magma, designed to perform the basic tasks related to ideals in number fields without pre-computing integral bases. It is based on Montes algorithm and a number of local techniques that we have developed in a series of papers in the last years.

math.NT↗