The emerging technology of quantum reservoir computing (QRC) stands out in the noisy-intermediate scale quantum era (NISQ) for its exceptional efficiency and adaptability. By harnessing the power of quantum computing, it holds a great potential to untangle complex economic markets, as demonstrated here in an application to food price crisis prediction - a critical effort in combating food waste and establishing sustainable food chains. Nevertheless, a pivotal consideration for its success is the optimal design of the quantum reservoirs, ensuring both high performance and compatibility with current devices. In this paper, we provide an efficient criterion for that purpose, based on the complexity of the reservoirs. Our results emphasize the crucial role of optimal design in the algorithm performance, especially in the absence of external regressor variables, showcasing the potential for novel insights and transformative applications in the field of time series prediction using quantum computing.

We consider a Hamiltonian system that models the scattering of helium atoms off a copper surface. The interaction between the He and the Cu atoms is described by a corrugated Morse potential. Using corrugation coefficients values in the potential obtained by fitting to experimental values, we prove that, provided some coefficient of an auxiliary function is different from 0, there are regions of the phase space, corresponding to sufficiently large energy of the incident atom, where the scattering is chaotic. Furthermore, we prove that the system has oscillatory motions.

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

In this work, we analyze the evolution of the phase-space structures of KCN molecular system as a function of the vibrational energy using Lagrangian descriptors. For low energies, the motion is mostly regular around the absolute minimum of the potential energy surface. As the energy increases, the phase space combines regions with regular and chaotic motion, a difference that is well captured by the Lagrangian descriptors. We show that the dynamics is mostly governed by the invariant manifolds of the stretch periodic orbits located at the top of one of the energetic barriers of the system. Furthermore, we show a perfect agreement between the bifurcation theory and the differences observed in the phase-space structures as the vibrational energy is modified. The accuracy of our calculations is also assessed by explicit comparison with the invariant manifolds computed using linear dynamics.

We study dynamical localization in an ultracold atom confined in an optical lattice that is simultaneously shaken by two competing pulsatile modulations with different amplitudes, periods, and waveforms. The effects of finite-width time pulses, modulation waveforms, and commensurable and incommensurable driving periods are investigated. We describe a particularly complex scenario and conclude that dynamical localization can survive, or even increase, when a periodic modulation is replaced by a quasiperiodic one of equal amplitude. Our analytical and numerical results indicate that there exists a strong correlation between the strengths of chaos (stochastic layer width) and dynamical localization (difference between the classical and quantum momentum dispersions) over the entire parameter space, which is maintained regardless of the periodic or quasiperiodic nature of the modulation. This persistent correlation provides a useful guide to optimally control the strength of dynamical localization by tuning the modulation parameters in real-world systems subjected to pulses of finite width.

Currently cryptocurrencies and Decentralized Finance (DeFi), which enable financial services on public blockchains, represents a new growing trend in finance. In contrast to financial markets, ruled by traditional corporations, DeFi is completely transparent as it keeps records of all transactions that occur in the network and makes them publicly available. The availability of the data represents an opportunity to analyze and understand the market from the complexity that emerges from the interactions of the actors (users, bots and companies) operating in the embedded market. In this paper we focus on the Ethereum network and our main goal is to show that the properties of the underlying transaction network provide further and useful information to forecast the evolution of the market. We aim to separate the non redundant effects of the blockchain transaction network properties from classic technical indicators and social media trends in the future price of Ethereum. To this end, we build two machine learning models to predict the future trend of the market. The first one serves as a base model and considers a set of the most relevant features according to the current scientific literature including technical indicators and social media trends. The second model considers the features of the base model, together with the network properties computed from the transaction networks. We found that the full model outperforms the base model and can anticipate 46 more rises in the price than the base model and 19 more falls.

The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of nonintegrable 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.

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.

Pairs trading is a short-term speculation trading strategy based on matching a long position with a short position in two assets in the hope that their prices will return to their historical equilibrium. In this paper, we focus on identifying opportunities where mean reversion will happen quickly, as the commission costs associated with keeping the positions open for an extended period of time can eliminate excess returns. To this end, we propose the use of the local Hurst exponent as a signal to open trades in the cryptocurrencies market. We conduct a natural experiment to show that the spread of pairs with anti-persistent values of Hurst revert to their mean significantly faster. Next, we verify that this effect is universal across pairs with different levels of co-movement. Finally, we back-test several pairs trading strategies that include H<0.5 as an indicator and check that all of them result in profits. Hence, we conclude that the Hurst exponent represents a meaningful indicator to detect pairs trading opportunities in the cryptocurrencies market.

Scar theory is one of the fundamental pillars in the field of quantum chaos, and scarred functions are a superb tool to carry out studies in it. Several methods, usually semiclassical, have been described to cope with these two phenomena. In this paper, we present an alternative method, based on the novel machine learning algorithm known as reservoir computing, to calculate such scarred wave functions together with the associated eigenstates of the system. The resulting methodology achieves outstanding accuracy while reducing execution times by a factor of ten. As an illustration of the effectiveness of this method, we apply it to the widespread chaotic two-dimensional coupled quartic oscillator.

We consider the classical approximation of a realistic model for the scattering of He atoms from Cu surfaces. For this problem, modeled by a two-degrees-of-freedom Hamiltonian system, the existence of chaos has been proven analytically very recently for sufficiently large values of the energy, if some quantity, known as the Stokes constant, is non-zero (Borondo et al., 2024). Taking two different and independent approaches, this paper provides numerical evidence that this is indeed the case. Both approaches provide the same value of the non-zero Stokes constant.

Recently, reservoir computing (RC) has emerged as one of the most effective algorithms to model and forecast volatile and chaotic time series. In this paper, we aim to contribute to the understanding of the uncertainty associated with the predictions made by RC models and to propose a methodology to generate RC prediction intervals. As an illustration, we analyze the error distribution for the RC model when predicting the price time series of several agri-commodities. Results show that the error distributions are best modeled using a Normal Inverse Gaussian (NIG). In fact, NIG outperforms the Gaussian distribution, as the latter tends to overestimate the width of the confidence intervals. Hence, we propose a methodology where, in the first step, the RC generates a forecast for the time series and, in the second step, the confidence intervals are generated by combining the prediction and the fitted NIG distribution of the RC forecasting errors. Thus, by providing confidence intervals rather than single-point estimates, our approach offers a more comprehensive understanding of forecast uncertainty, enabling better risk assessment and more informed decision-making in business planning based on forecasted prices.

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.

The biggest challenge that quantum computing and quantum machine learning are currently facing is the presence of noise in quantum devices. As a result, big efforts have been put into correcting or mitigating the induced errors. But, can these two fields benefit from noise? Surprisingly, we demonstrate that under some circumstances, quantum noise can be used to improve the performance of quantum reservoir computing, a prominent and recent quantum machine learning algorithm. Our results show that the amplitude damping noise can be beneficial to machine learning, while the depolarizing and phase damping noises should be prioritized for correction. This critical result sheds new light into the physical mechanisms underlying quantum devices, providing solid practical prescriptions for a successful implementation of quantum information processing in nowadays hardware.

The so-called soil-landscape model is the central paradigm which relates soil types to their forming factors through the visionary Jenny's equation. This is a formal mathematical expression that would permit to infer which soil should be found in a specific geographical location if the involved relationship was sufficiently known. Unfortunately, Jenny's is only a conceptual expression, where the intervening variables are of qualitative nature, not being then possible to work it out with standard mathematical tools. In this work, we take a first step to unlock this expression, showing how Machine Learning can be used to predictably relate soil types and environmental factors. Our method outperforms other conventional statistical analyses that can be carried out on the same forming factors defined by measurable environmental variables.

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)0031-900710.1103/PhysRevLett.80.944] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing the Planck constant, we induced a transition from order to chaos, in which scarred wave functions 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 straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.

In this work, we identify the phase-space structures which are responsible for the chaotic dynamics observed in KCN molecular system using the Lagrangian descriptors. We show that the vibrational dynamics of this molecule is strongly determined by the invariant manifolds associated with a particular stretching periodic orbit previously described (Parraga et al., 2018). Likewise, the representation of these invariant manifolds on a Poincare surface of section is also studied, concluding that the intricate depiction that is observed has its origin in the complex behavior of the manifolds, which is a consequence of the strong anharmonicities in the potential energy surface.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Stability and chaoticity in conservative Hamiltonian systems are analyzed using an indicator based on a generalization of the virtual work principle (VWP) for Riemannian manifolds. The geometrodynamic formalism obtained in this way is applied to define a mechanical manifold using the Jacobi metric, where the system trajectories are geodesics. The VWP for static mechanical equilibrium in Euclidean spaces is generalized and applied to trajectories in this manifold through geodesic equations derived from a Weyl transformation to this metric. We further interpret each trajectory of the system as a curve representing a non-stretchable string under tension derived from a potential function with constant length in this mechanical manifold, and analyze its stability through the fluctuation of an observable defined from the previous analysis. In this way, we can define a practical chaos indicator and find a sufficiency condition for a conservative dynamical system to have a regular dynamics. Several benchmark cases in two and three dimensions are presented as illustrations.

Anticipating price crises in the market of agri-commodities is critical to guarantee both the sustainability of the food system and to ensure food security. However, this is not an easy task, since the problem implies analyzing small and very volatile time series, which are highly influenced by external factors. In this paper, we show that suitable reservoir computing algorithms can be developed that outperform traditional approaches, by reducing the Mean Absolute Error and, more importantly, increasing the Market Direction Accuracy. For this purpose, the applicability of five variants of such method to forecast this market is explored, and their performance evaluated by comparing the results with those obtained with the standard LSTM and SARIMA benchmarks. We conclude that decomposing the time series and modeling each component with a separate RC is essential to successfully anticipate price trends, and that this method works even in the complex changing temporal scenario of the Covid-19 pandemic, when part of the data were collected.