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Abstract Developing the field of neuromorphic quantum computing necessitates designing scalable quantum memory devices. Here, we propose a superconducting quantum memory device in the microwave regime, termed a microwave quantum memcapacitor. It comprises two linked resonators, the primary one is coupled to a Superconducting Quantum Interference Device, which allows for the modulation of the resonator properties through external magnetic flux. The auxiliary resonator, operated through weak measurements, provides feedback to the primary resonator, ensuring stable memory behavior. This device operates with a classical input in one cavity while reading the response in the other, serving as a fundamental building block toward arrays of microwave quantum memcapacitors. We observe that a bipartite setup can retain its memory behavior and gains entanglement and quantum correlations. Our findings pave the way for the experimental implementation of memcapacitive superconducting quantum devices and memory device arrays for neuromorphic quantum computing.

The quantum Rabi model describes the coupling of a two-state system to a bosonic field mode. Recent theoretical work has pointed out that a generalized periodic version of this model, which maps onto Hamiltonians applicable in superconducting qubit settings, can be quantum simulated with cold trapped atoms. Here, we experimentally demonstrate atomic dynamics predicted by the periodic quantum Rabi model far in the deep strong-coupling regime. The two-state system is represented by two Bloch bands of cold atoms in an optical lattice, and the bosonic mode by oscillations in a superimposed optical dipole trap potential. The observed dynamics beyond the usual quantum Rabi physics becomes relevant when the edge of the Brillouin zone is reached, and evidence for collapse and revival of the initial state is revealed at extreme coupling conditions.

Light interaction with atoms depends on the strength of the light-matter coupling and the energy splitting of the modes involved. Here the authors study of quantum Rabi dynamics in a deep strong coupling regime by using a cloud of cold rubidium atoms.

A novel methodology that leverages physics-informed neural networks to optimize quantum circuits in systems with $\mathrm{N}_{\mathrm{Q}}$ qubits by addressing the counterdiabatic (CD) protocol is introduced. The primary purpose is to employ physics-inspired deep learning techniques for accurately modeling the time evolution of various physical observables within quantum systems. To achieve this, we integrate essential physical information into an underlying neural network to effectively tackle the problem. Specifically, the imposition of the solution to meet the principle of least action, along with the hermiticity condition on all physical observables, among others, ensuring the acquisition of appropriate CD terms based on underlying physics. This approach provides a reliable alternative to previous methodologies relying on classical numerical approximations, eliminating their inherent constraints. The proposed method offers a versatile framework for optimizing physical observables relevant to the problem, such as the scheduling function, gauge potential, temporal evolution of energy levels, among others. This methodology has been successfully applied to 2-qubit representing $\mathrm{H}_{2}$ molecule using the STO-3G basis, demonstrating the derivation of a desirable decomposition for non-adiabatic terms through a linear combination of Pauli operators. This attribute confers significant advantages for practical implementation within quantum computing algorithms.

Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest rates are assumed is governed by the Black-Scholes model, a linear parabolic partial differential equation with terminal value given by the payoff of the option contract and no additional boundary conditions. Here, we present a digital quantum algorithm to solve the Black-Scholes equation on a quantum computer by mapping it to the Schrödinger equation. The non-Hermitian nature of the resulting Hamiltonian is solved by embedding its propagator into an enlarged Hilbert space by using only one additional ancillary qubit. Moreover, due to the choice of periodic boundary conditions, given by the definition of the discretized momentum operator, we duplicate the initial condition, which substantially improves the stability and performance of the protocol. The algorithm shows a feasible approach for using efficient Hamiltonian simulation techniques as quantum signal processing to solve the price dynamics of financial derivatives on a digital quantum computer. Our approach differs from those based on Monte Carlo integration, exclusively focused on sampling the solution assuming the dynamics is known. We report expected accuracy levels comparable to classical numerical algorithms by using nine qubits to simulate its dynamics on a fault-tolerant quantum computer, and an expected success probability of the post-selection procedure due to the embedding protocol above 60%.

We consider the propagation of phonons in the presence of a particle sink with radial flow in a Bose–Einstein condensate. Because the particle sink can be used to simulate a static acoustic black hole, the phonon would experience a considerable spacetime curvature at appreciable distance from the sink. The trajectory of the phonons is bended after passing by the particle sink, which can be used as a simulation of the gravitational lensing effect in a Bose–Einstein condensate. Possible experimental implementations are discussed.

We propose digitized-counterdiabatic quantum optimization (DCQO) to achieve polynomial enhancement over adiabatic quantum optimization for the general Ising spin-glass model, which includes the whole class of combinatorial optimization problems. This is accomplished via the digitization of adiabatic quantum algorithms that are catalyzed by the addition of nonstoquastic counterdiabatic terms. The latter is suitably chosen not only for escaping classical simulability, but also for speeding up the performance. Finding the ground state of a general Ising spin-glass Hamiltonian is used to illustrate that the inclusion of k-local nonstoquastic counterdiabatic terms can always outperform the traditional adiabatic quantum optimization with stoquastic Hamiltonians. In particular, we show that a polynomial enhancement in the ground-state success probability can be achieved for a finite-time evolution, even with the simplest two-local counterdiabatic terms. Furthermore, the considered digitization process within the gate-based quantum computing paradigm, provides the flexibility to introduce arbitrary nonstoquastic interactions. As an experimental test, we study the performance of the DCQO algorithm on cloud-based IBM's superconducting and Quantinuum's ion-trap quantum processors with up to 8 qubits. Along these lines, using our proposed paradigm on current noisy intermediate-scale quantum (NISQ) computers, quantum speedup may be reached to find approximate solutions for NP-complete and NP-hard optimization problems. We expect DCQO to become a fast-lane paradigm toward quantum advantage in the NISQ era.

Abstract Nine point sources appeared within half an hour on a region within $$\sim $$ ∼ 10 arcmin of a red-sensitive photographic plate taken in April 1950 as part of the historic Palomar Sky Survey. All nine sources are absent on both previous and later photographic images, and absent in modern surveys with CCD detectors which go several magnitudes deeper. We present deep CCD images with the 10.4-m Gran Telescopio Canarias, reaching brightness $$r \sim 26$$ r ∼ 26 mag, that reveal possible optical counterparts, although these counterparts could equally well be just chance projections. The incidence of transients in the investigated photographic plate is far higher than expected from known detection rates of optical counterparts to e.g. flaring dwarf stars, Fast Radio Bursts, Gamma Ray Bursts or microlensing events. One possible explanation is that the plates have been subjected to an unknown type of contamination producing mainly point sources with of varying intensities along with some mechanism of concentration within a radius of $$\sim $$ ∼ 10 arcmin on the plate. If contamination as an explanation can be fully excluded, another possibility is fast (t $$

We studied the tunable control of the non-Markovianity of a bosonic mode due to its coupling to a set of auxiliary qubits, both embedded in a thermal reservoir. Specifically, we considered a single cavity mode coupled to auxiliary qubits described by the Tavis–Cummings model. As a figure of merit, we define the dynamical non-Markovianity as the tendency of a system to return to its initial state, instead of evolving monotonically to its steady state. We studied how this dynamical non-Markovianity can be manipulated in terms of the qubit frequency. We found that the control of the auxiliary systems affects the cavity dynamics as an effective time-dependent decay rate. Finally, we show how this tunable time-dependent decay rate can be tuned to engineer bosonic quantum memristors, involving memory effects that are fundamental for developing neuromorphic quantum technologies.

The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, benchmarking its performance for attaining a financial equilibrium. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed into a spin-1/2 Hamiltonian with at most, two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. The size of the simulation is mainly constrained by the necessity of a large number of physical qubits representing a logical qubit with the correct connectivity. Our experiment paves the way for the codification of this quantitative macroeconomics problem in quantum annealers.

We propose a protocol to encode classical bits in the measurement statistics of many-body Pauli observables, leveraging quantum correlations for a random access code. Measurement contexts built with these observables yield outcomes with intrinsic redundancy, something we exploit by encoding the data into a set of convenient context eigenstates. This allows to randomly access the encoded data with few resources. The eigenstates used are highly entangled and can be generated by a discretely-parametrized quantum circuit of low depth. Applications of this protocol include algorithms requiring large-data storage with only partial retrieval, as is the case of decision trees. Using $n$-qubit states, this Quantum Random Access Code has greater success probability than its classical counterpart for $n\ge 14$ and than previous Quantum Random Access Codes for $n \ge 16$. Furthermore, for $n\ge 18$, it can be amplified into a nearly-lossless compression protocol with success probability $0.999$ and compression ratio $O(n^2/2^n)$. The data it can store is equal to Google-Drive server capacity for $n= 44$, and to a brute-force solution for chess (what to do on any board configuration) for $n= 100$.

The Vanishing & Appearing Sources during a Century of Observations (VASCO) project investigates astronomical surveys spanning a time interval of 70 years, searching for unusual and exotic transients. We present herein the VASCO Citizen Science Project, which can identify unusual candidates driven by three different approaches: hypothesis, exploratory, and machine learning, which is particularly useful for SETI searches. To address the big data challenge, VASCO combines three methods: the Virtual Observatory, user-aided machine learning, and visual inspection through citizen science. Here we demonstrate the citizen science project and its improved candidate selection process, and we give a progress report. We also present the VASCO citizen science network led by amateur astronomy associations mainly located in Algeria, Cameroon, and Nigeria. At the moment of writing, the citizen science project has carefully examined 15,593 candidate image pairs in the data (ca. 10% of the candidates), and has so far identified 798 objects classified as “vanished”. The most interesting candidates will be followed up with optical and infrared imaging, together with the observations by the most potent radio telescopes.

Simulation of quantum field theory using quantum systems would in principle allow avoidance of the exponential overhead required for classical simulations. Here, the authors use a multilevel trapped ion to simulate the processes of self-interaction and particle-antiparticle creation/annihilation.

Abstract We measure multi-time correlation functions of a set of Pauli operators on a two-level system, which can be used to retrieve its associated linear response functions. The two-level system is an effective spin constructed from the nuclear spins of 1H atoms in a solution of 13C-labeled chloroform. Response functions characterize the linear response of the system to a family of perturbations, allowing us to compute physical quantities such as the magnetic susceptibility of the effective spin. We use techniques exported from quantum information to measure time correlations on the two-level system. This approach requires the use of an ancillary qubit encoded in the nuclear spins of the 13C atoms and a sequence of controlled operations. Moreover, we demonstrate the ability of such a quantum platform to compute time-correlation functions of arbitrary order, which relate to higher-order corrections of perturbative methods. Particularly, we show three-time correlation functions for arbitrary times, and we also measure time correlation functions at fixed times up to tenth order.

Abstract We study two dispersive regimes of the Dicke model in the dynamics of N two-level atoms interacting with a bosonic mode for long interaction times. Firstly, we analyze the model for the regime in which the qubit frequencies are equal and smaller than the mode frequency, and for values of the coupling strength similar or larger than the mode frequency, namely, the deep strong coupling regime. Secondly, we address an interaction that is dependent on the photon number, where the coupling strength is comparable to the geometric mean of the qubit and mode frequencies. We show that the associated dynamics is analytically tractable and provide useful frameworks with which to analyze the system behavior. In the deep strong coupling regime, we unveil the structure of unexpected resonances for specific values of the coupling, present for N ≥ 2, and in the photon-number-dependent regime we demonstrate that all the nontrivial dynamical behavior occurs in the atomic degrees of freedom for a given Fock state. We verify these assertions with numerical simulations of the qubit population and photon-statistic dynamics.

Abstract A single-ion reservoir has been tested, and characterized in order to be used as a highly sensitive optical detector of electric signals arriving at the trapping electrodes. Our system consists of a single laser-cooled 40Ca+ ion stored in a Paul trap with rotational symmetry. The performance is observed through the axial motion of the ion, which is equivalent to an underdamped and forced oscillator. Thus, the results can be projected also to Penning traps. We have found that, for an ion oscillator temperature T axial ≲ 10 mK in the forced-frequency range ω z = 2π × (80,200 kHz), the reservoir is sensitive to a time-varying electric field equivalent to an electric force of 5.3(2) neV/μm, for a measured quality factor Q = 3875(45), and a decay time constant γ z = 88(2) s−1. This method can be applied to measure optically the strength of an oscillating field or induced (driven) charge in this frequency range within times of tens of milliseconds. Furthermore the ion reservoir has been proven to be sensitive to electrostatic forces by measuring the ion displacement. Since the heating rate is below 0.3 μeV/s, this reservoir might be used as optical detector for any ion or bunch of charged particles stored in an adjacent trap.

Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. In its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between the number of noisy factors considered and the computational time to perform a numerical simulation. Here, we employ the quantum principal component analysis to reduce the number of noisy factors required to accurately simulate the time evolution of several time-maturing forward rates. The principal components are experimentally estimated with the five-qubit IBMQX2 quantum computer for 2×2 and 3×3 cross-correlation matrices, which are based on historical data for two and three time-maturing forward rates. This paper is a step towards the design of a general quantum algorithm to fully simulate on quantum computers the Heath-Jarrow-Morton model for pricing interest-rate financial derivatives. It shows indeed that practical applications of quantum computers in finance will be achievable in the near future.

Quantum computers based on superconducting circuits are experiencing rapid development, with the aim to outperform classical computers in certain useful tasks in the near future. However, the currently available chip fabrication technologies limit the capability of gathering a large number of high-quality qubits in a single superconducting chip, a requirement for implementing quantum error correction. Furthermore, achieving high connectivity in a chip poses a formidable technological challenge. Here, we propose a hybrid digital-analog quantum algorithm that enhances the physical connectivity among qubits coupled by an arbitrary inhomogeneous nearest-neighbor Ising Hamiltonian and generates an arbitrary all-to-all Ising Hamiltonian only by employing single-qubit rotations. Additionally, we optimize the proposed algorithm in the number of analog blocks and in the time required for the simulation. These results take advantage of the natural evolution of the system by combining the flexibility of digital steps with the robustness of analog quantum computing, allowing us to improve the connectivity of the hardware and the efficiency of quantum algorithms.

Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the noisy intermediate-scale quantum era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.

The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and conductances. These conductances depend on previous depolarizing membrane voltages, which can be identified with a memory resistive element called memristor. Inspired by the recent quantization of the memristor, a simplified Hodgkin-Huxley model including a single ion channel has been studied in the quantum regime. Here, we study the quantization of the complete Hodgkin-Huxley model, accounting for all three ion channels, and introduce a quantum source, together with an output waveguide as the connection to a subsequent neuron. Our system consists of two memristors and one resistor, describing potassium, sodium, and chloride ion channel conductances, respectively, and a capacitor to account for the axon's membrane capacitance. We study the behavior of both ion channel conductivities and the circuit voltage, and we compare the results with those of the single channel, for a given quantum state of the source. It is remarkable that, in opposition to the single-channel model, we are able to reproduce the voltage spike in an adiabatic regime. Arguing that the circuit voltage is a quantum variable, we find a purely quantum-mechanical contribution in the system voltage's second moment. This work represents a complete study of the Hodgkin-Huxley model in the quantum regime, establishing a recipe for constructing quantum neuron networks with quantum state inputs. This paves the way for advances in hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise.

Quantum simulations consist in the intentional reproduction of physical or unphysical models into another more controllable quantum system. Beyond establishing communication vessels between unconnected fields, they promise to solve complex problems which may be considered as intractable for classical computers. From a historic perspective, two independent approaches have been pursued, namely, digital and analog quantum simulations. The former usually provide universality and flexibility, while the latter allows for better scalability. Here, we review recent literature merging both paradigms in the context of superconducting circuits, yielding: digital-analog quantum simulations. In this manner, we aim at getting the best of both approaches in the most advanced quantum platform involving superconducting qubits and microwave transmission lines. The discussed merge of quantum simulation concepts, digital and analog, may open the possibility in the near future for outperforming classical computers in relevant problems, enabling the reach of a quantum advantage.

Introduction. This article’s purpose is to report a case where maxillary lateral incisors and mandibular central incisors are extracted and a canine substitution was performed as the best therapeutic option in order to obtain symmetry in a malocclusion with an upper lateral incisor with poor prognostic, solve moderate crowding, get enough space for the permanent dentition, and provide stability to the results. Case Report. An 11-year-old boy with straight profile with acute-to-normal nasolabial angle and protruded lips, mixed dentition, lower and upper severe crowding, and a bilateral molar angle Class I. The left maxillary lateral incisor failed endodontic treatment secondary to an intrusive traumatic lesion in the primary and permanent dentition. The treatment of choice was the extraction of both upper lateral incisors and both central lower incisors. The patient finished with molar and canine angle Class I and coincident midlines and was functionally stable; both lateral and protrusive jaw movements were effectively made by the first premolars and central incisors and canines without improper contacts of the rest of the teeth. Overbite of one-third and correct overjet were also achieved, and the esthetic outcome was satisfactory due to the composed material restorations of both the central and lateral incisors, as well as recontouring of the first maxillary premolars.

The paradigmatic spin-boson model considers a spin degree of freedom interacting with an environment typically constituted by a continuum of bosonic modes. This ubiquitous model is of relevance in a number of physical systems where, in general, one has neither control over the bosonic modes, nor the ability to tune distinct interaction mechanisms. Despite this apparent lack of control, we present a suitable transformation that approximately maps the spin-boson dynamics into that of a tunable multiphoton Jaynes-Cummings model undergoing dissipation. Interestingly, the latter model describes the coherent interaction between a spin and a single bosonic mode via the simultaneous exchange of n bosons per spin excitation. Resorting to the so-called reaction coordinate method, we identify a relevant collective bosonic mode in the environment, which is then used to generate multiphoton interactions following the proposed theoretical framework. Moreover, we show that spin-boson models featuring structured environments can lead to non-Markovian multiphoton Jaynes-Cummings dynamics. We discuss the validity of the proposed method depending on the parameters and analyse its performance, which is supported by numerical simulations. In this manner, the spin-boson model serves as a good analogue quantum simulator for the inspection and realization of multiphoton Jaynes-Cummings models, as well as the interplay of non-Markovian effects and, thus, as a simulator of light-matter systems with tunable interaction mechanisms.

We propose a method to generate nonclassical states of light in multimode microwave cavities. Our approach considers two-photon processes that take place in a system composed of N extended cavities and an ultrastrongly coupled light–matter system. Under specific resonance conditions, our method generates, in a deterministic manner, product states of uncorrelated photon pairs, Bell states, and W states in different modes on the extended cavities. Furthermore, the numerical simulations show that the generation scheme exhibits a collective effect which decreases the generation time in the same proportion as the number of extended cavity increases. Moreover, the entanglement encoded in the photonic states can be transferred towards ancillary two-level systems to generate genuine multipartite entanglement. Finally, we discuss the feasibility of our proposal in circuit quantum electrodynamics. This proposal could be of interest in the context of quantum random number generator, due to the quadratic scaling of the output state.

A Penning-trap facility for high-precision mass spectrometry based on a novel detection method has been built. This method consists in measuring motional frequencies of singly-charged ions trapped in strong magnetic fields through the fluorescence photons from laser-cooled ^40 Ca ^+ ions, to overcome limitations faced in electronic single-ion detection techniques. The key element of this facility is an open-ring Penning trap coupled upstream to a preparation Penning trap similar to those used at Radioactive Ion Beam facilities. Here we present a full characterization of the trap and demonstrate motional frequency measurements of trapped ions stored by applying external radiofrequency fields in resonance with the ions’ eigenmotions, in combination with time-of-flight identification. The infrastructure developed to observe the fluorescence photons from ^40 Ca ^+ , comprising the 12 laser beams and the optical system to register the image in a high-sensitive CCD sensor, has been proved by taking images of the trapped and cooled ^40 Ca ^+ ions. This demonstrates the functionality of the proposed laser-based mass-spectrometry technique, providing a unique platform for precision experiments with implications in different fields of physics.

En el nuevo contexto del Espacio Europeo de Educación Superior, se presentan los resultados obtenidos por los diez profesores responsables de un Proyecto de Innovación Docente auspiciado por la Universidad de Córdoba en los cursos 2007-2009. Concebido básicamente como una reflexión sobre el propio quehacer del docente, aquél se planteó cómo explicar el poder en la época Moderna desde distintas disciplinas y, sobre todo, cómo el alumnado, variado por cursos y nivel de formación, trabajó y valoró la propuesta. Metodología eminentemente práctica y apoyo en las nuevas tecnologías han permitido agilizar el estudio y considerar muy positiva la experiencia obtenida.

The dynamical Casimir effect is an intriguing phenomenon in which photons are generated from vacuum due to a non-adiabatic change in some boundary conditions. In particular, it connects the motion of an accelerated mechanical mirror to the generation of photons. While pioneering experiments demonstrating this effect exist, a conclusive measurement involving a mechanical generation is still missing. We show that a hybrid system consisting of a piezoelectric mechanical resonator coupled to a superconducting cavity may allow to electro-mechanically generate measurable photons from vacuum, intrinsically associated to the dynamical Casimir effect. Such an experiment may be achieved with current technology, based on film bulk acoustic resonators directly coupled to a superconducting cavity. Our results predict a measurable photon generation rate, which can be further increased through additional improvements such as using superconducting metamaterials.

The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong-coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong-coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back and forth when the coupling reaches the deep strong-coupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong-coupling regime.

En el nuevo contexto del Espacio Europeo de Educación Superior, se presentan los resultados obtenidos por los diez profesores responsables de un Proyecto de Innovación Docente auspiciado por la Universidad de Córdoba en los cursos 2007-2009. Concebido básicamente como una reflexión sobre el propio quehacer del docente, aquél se planteó cómo explicar el poder en la época Moderna desde distintas disciplinas y, sobre todo, cómo el alumnado, variado por cursos y nivel de formación, trabajó y valoró la propuesta. Metodología eminentemente práctica y apoyo en las nuevas tecnologías han permitido agilizar el estudio y considerar muy positiva la experiencia obtenida

RESUMEN: En este artículo se analizan las relaciones entre el reino de Aragón y la monarquía de los Austrias en el ámbito de la colaboración aragonesa en las empresas militares de la Corona durante este periodo. Aunque las relaciones fueron generalmente amistosas, éstas no estuvieron exentas de problemas y disputas cuando la Corona demandaba subsidios. Las solicitudes de los Austrias planteadas sobre Aragón a lo largo del siglo XVI, experimentarían un notable incremento en la centuria siguiente. La nueva apertura del conflicto con Francia en 1635 y, especialmente, la Guerra de Cataluña producida entre 1640 y 1652 obligaron a los Austrias a volcarse sobre sus reinos en solicitud de ayuda financiera y asistencia militar. El avance de las armas francesas y la invasión de Aragón, sucedida en 1641, alarmaron a la monarquía hispánica. Los aragoneses fueron requeridos para apoyar los nuevos planes de la Monarquía bajo la premisa de hacerlo en «defensa del Reino». Las demandas de la Corona continuaron durante toda la centuria hasta la llegada de los Borbones al poder, lo que representaba la abolición de los fueros aragoneses en 1711.ABSTRACT: The purpose of this article is to outline the relations between the kingdom of Aragon and the Habsburg monarchy regarding Aragonese collaboration in the military expedition during the Habsburg period. Despite the fact that relations were mainly friendly, some troubles and disputes existed when the Spanish monarch asked for subsidies. Habsburgs royal demands on the reign of Aragon in the sixteenth century reached an important. increasing during the next century. The renewal of war with France in 1635 and, especially, the War of Catalonia between 1640 and 1652 compelled Habsburgs to ask his kingdoms for financial support and military assistance. The progress of French arms and the invasion of Aragon happened in 1641 alarmed the Spanish monarchy. The Aragonese were called upon to support the new plans of the monarchy under the argument of «defence of the realm». Royal demands even continued along the century up to the Bourbons took power and caused the abolition of the Aragonese ordinances in 1711.

We introduce the works collected in the focus issue on Cavity and circuit quantum quantum electrodynamics in solids.

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