arXiv subjects

Gabriel G. Carlo

Publications and source records attributed to Gabriel G. Carlo.

At least 19 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

Complex spacing ratio statistics in the partially open asymmetric quantum baker map

We study the complex eigenvalue statistics of the asymmetric quantum baker map with partial projective openings. The classical asymmetric baker map, with its discontinuity at $q=2/3$, is fully chaotic, has no reflection symmetry, and provides a clean setting with tunable escape rate and fractal repeller dimension. We consider three distinct opening geometries in position space: localized (contiguous channels), random, and uniform (equispaced channels), all controlled by a tunable amplitude reflectivity parameter $ρ$ that interpolates between the fully open ($ρ=0$) and the closed ($ρ=1$) limits. We use the partially truncated circular unitary ensemble (PTCUE) as the random matrix theory benchmark. The main focus is on the joint distribution of the complex spacing ratio $z$, defined as the ratio of the distances from an eigenvalue to its nearest and next-nearest neighbors in the complex plane. We find a smooth crossover from a quasi-1D spectral regime, where eigenvalues cluster near the unit circle and the phase distribution of $z$ is peaked, to a two-dimensional Ginibre-like regime, where the distribution becomes nearly uniform and level repulsion is fully developed. Both the number of open channels $M$ and the reflectivity $ρ$ modulate this crossover, and $ρ$ provides an additional continuous control even at fixed opening size. All three opening models converge to PTCUE statistics at large $M$, while differences are most pronounced for the localized model at small $M$. No evidence of an abrupt transition is found. This crossover which suggests a universal behavior, has deep consequences for open quantum and wave-chaotic experiments.

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

The simplest 2D quantum walk detects chaoticity

Quantum walks are at present an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior. For this purpose, we consider an extremely simple model consisting of alternating one-dimensional walks along the two spatial coordinates in bidimensional closed domains (hard wall billiards). The chaotic or regular behavior induced by the boundary shape in the deterministic classical motion translates into chaotic signatures for the quantized problem, resulting in sharp differences in the spectral statistics and morphology of the eigenfunctions of the quantum walker. Indeed, we found for the Bunimovich stadium -- a chaotic billiard -- level statistics described by a Brody distribution with parameter $δ\simeq 0.1$. This indicates a weak level repulsion, and also enhanced eigenfunction localization, with an average participation ratio (PR) $\simeq$ 1150) compared to the rectangular billiard (regular) case, where the average PR $\simeq$ 1500. Furthermore, scarring on unstable periodic orbits is observed. The fact that our simple model exhibits such key signatures of quantum chaos, e.g., non-Poissonian level statistics and scarring, that are sensitive to the underlying classical dynamics in the free particle billiard system is utterly surprising, especially when taking into account that quantum walks are diffusive models, which are not direct quantizations of a Hamiltonian.

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

Ideal Gas Law for a Quantum Particle

The question of how classical thermodynamic laws emerge from the underlying quantum substrate lies at the foundations of physics. Here, we examine the validity of the ideal gas law (IGL) for a single quantum particle confined within a two-dimensional cavity. By interpreting the quantum wave function as a probability density analogous to that of an ideal gas, we employ the energy equipartition principle to define the temperature of the quantum state. For the mean pressure we take two definitions, one straightforwardly based on the radiation pressure concept and the other taking advantage of a quasi-orthogonality relation valid for billiard eigenstates. We analyze systems with regular dynamics-the circular and rectangular billiards-and compare them with the classically chaotic Bunimovich stadium. We find that the IGL for the first definition of pressure holds exactly in isotropic systems (as the circular case), while for anisotropic geometries, quantum eigenfunctions generally conform to the IGL only on average, exhibiting meaningful deviations. These deviations are diminished in the presence of chaotic dynamics and for coherent states. This observation is consistent with the Eigenstate Thermalization Hypothesis (ETH). Notably, the second definition of pressure allows for a good matching with the IGL.

quant-ph↗

arXiv2025

Spectral truncation of out-of-time-ordered correlators in dissipative system

Out-of-time-ordered correlators (OTOCs) have emerged as powerful tools for diagnosing quantum chaos and information scrambling. While extensively studied in closed quantum systems, their behavior in dissipative environments remains less understood. In this work, we investigate the spectral decomposition of OTOCs in open quantum systems, using the dissipative modified kicked rotator (DMKR) as a paradigmatic model. By analyzing the eigenvalue spectrum of the quantum Liouvillian, we identify a crucial spectral truncation criterion that enables efficient modeling of OTOC dynamics. Our results reveal two distinct temporal regimes: a long-time decay phase governed by the spectral gap and an intermediate-time regime where a small subset of subdominant eigenvalues plays a crucial role. This spectral truncation criterion allows for efficient modeling of OTOC decay and reveals a direct connection between eigenvalue structure and information scrambling. Our results provide a quantitative framework for understanding OTOCs in dissipative quantum systems and suggest new avenues for experimental exploration in open quantum platforms.

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

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↗

arXiv2023

Quantum reservoir complexity by Krylov evolution approach

Quantum reservoir computing algorithms recently emerged as a standout approach in the development of successful methods for the NISQ era, because of its superb performance and compatibility with current quantum devices. By harnessing the properties and dynamics of a quantum system, quantum reservoir computing effectively uncovers hidden patterns in data. However, the design of the quantum reservoir is crucial to this end, in order to ensure an optimal performance of the algorithm. In this work, we introduce a precise quantitative method, with strong physical foundations based on the Krylov evolution, to assess the wanted good performance in machine learning tasks. Our results show that the Krylov approach to complexity strongly correlates with quantum reservoir performance, making it a powerful tool in the quest for optimally designed quantum reservoirs, which will pave the road to the implementation of successful quantum machine learning methods.

quant-ph↗

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↗

arXiv2023

Majorization-based benchmark of the complexity of quantum processors

Here we investigate the use of the majorization-based indicator introduced in [R. O. Vallejos, F. de Melo, and G. G. Carlo, Phys. Rev. A 104, 012602 (2021)] as a way to benchmark the complexity within reach of quantum processors. By considering specific architectures and native gate sets of currently available technologies, we numerically simulate and characterize the operation of various quantum processors. We characterize their complexity for different native gate sets, qubit connectivity and increasing number of gates. We identify and assess quantum complexity by comparing the performance of each device against benchmark lines provided by randomized Clifford circuits and Haar-random pure states. In this way, we are able to specify, for each specific processor, the number of native quantum gates which are necessary, on average, for achieving those levels of complexity. Lastly, we study the performance of the majorization-based characterization in the presence of distinct types of noise. We find that the majorization-based benchmark holds as long as the circuits' output states have, on average, high purity ($\gtrsim 0.9$). In such cases, the indicator showed no significant differences from the noiseless case.

quant-ph↗

arXiv2022

Quantum Lyapunov exponent in dissipative systems

The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems. However, there are very few studies for open systems and they are mainly focused on isolating the effects of scrambling from those of decoherence. Adopting a different point of view, we study the interplay between these two processes. This proves crucial in order to explain the OTOC behavior when a phase space contracting dissipation is present, ubiquitous not only in real life quantum devices but in the dynamical systems area. The OTOC decay rate is closely related to the classical Lyapunov exponent -- with some differences -- and more sensitive in order to distinguish the chaotic from the regular behavior than other measures. On the other hand, it reveals as a generally simple function of the longest lived eigenvalues of the quantum evolution operator. We find no simple connection with the Ruelle-Pollicott resonances, but by adding Gaussian noise of $\hbar_{\text{eff}}$ size to the classical system we recover the OTOC decay rate, being this a consequence of the correspondence principle put forward in [Physical Review Letters 108 210605 (2012) and Physical Review E 99 042214 (2019)]

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↗

arXiv2021

The principle of majorization: application to random quantum circuits

We test the principle of majorization [J. I. Latorre and M. A. Martin-Delgado, Phys. Rev. A 66, 022305 (2002)] in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. The studied families are: {CNOT, H, T}, {CNOT, H, NOT}, {CNOT, H, S} (Clifford), matchgates, and IQP (instantaneous quantum polynomial-time). We verified that all the families of circuits satisfy on average the principle of decreasing majorization. In most cases the asymptotic state (number of gates going to infinity) behaves like a random vector. However, clear differences appear in the fluctuations of the Lorenz curves associated to asymptotic states. The fluctuations of the Lorenz curves discriminate between universal and non-universal classes of random quantum circuits, and they also detect the complexity of some non-universal but not classically efficiently simulatable quantum random circuits. We conclude that majorization can be used as a indicator of complexity of quantum dynamics, as an alternative to, e.g., entanglement spectrum and out-of-time-order correlators (OTOCs).

quant-ph↗

arXiv2020

Jaynes-Cummings model under monochromatic driving

We study analytically and numerically the properties of Jaynes-Cummings model under monochromatic driving. The analytical results allow to understand the regime of two branches of multi-photon excitation in the case of close resonance between resonator and driven frequencies. The rotating wave approximation allows to reduce the description of original driven model to an effective Jaynes-Cummings model with strong coupling between photons and qubit. The analytical results are in a good agreement with the numerical ones even if there are certain deviations between the theory and numerics in the close vicinity of the resonance. We argue that the rich properties of driven Jaynes-Cummings model represent a new area for experimental investigations with superconducting qubits and other systems.

quant-ph↗

arXiv2020

Relevant OTOC operators: footprints of the classical dynamics

The out-of-time order correlator (OTOC) has recently become relevant in different areas where it has been linked to scrambling of quantum information and entanglement. It has also been proposed as a good indicator of quantum complexity. In this sense, the OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. Here we have studied the OTOC-RE correspondence on physically meaningful bases like the ones constructed with the Pauli, reflection, and translation operators. The evolution is given by a paradigmatic bi-partite system consisting of two perturbed and coupled Arnold cat maps with different dynamics. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy and hence to reveal the character of the dynamics, up to a time t 0 . In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time. When represented in phase space, each one of these sets reveals the classical dynamical footprints with different depth according to the chosen base.

quant-ph↗