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The behavior of a collection of identical particles is intimately linked to the symmetries of their wavefunction under particle exchange. Topological anyons, arising as quasiparticles in low-dimensional systems, interpolate between bosons and fermions, picking up a complex phase when exchanged. Recent research has demonstrated that similar statistical behavior can arise with mixtures of bosonic and fermionic pairs, offering theoretical and experimental simplicity. We introduce an alternative implementation of such statistical anyons, based on promoting or suppressing the population of symmetric states via a symmetry generating Hamiltonian. The scheme has numerous advantages: anyonic statistics emerge in a single particle pair, extending straightforwardly to larger systems; the statistical properties can be dynamically adjusted; and the setup can be simulated efficiently. We show how exchange symmetry can be exploited to improve the performance of heat engines, and demonstrate a reversible work extraction cycle in which bosonization and fermionization replace compression and expansion strokes. Additionally, we investigate emergent thermal properties, including critical phenomena, in large statistical anyon systems., Comment: 21 pages, 11 figures

An intriguing phenomenon in non-equilibrium quantum thermodynamics is the asymmetry of thermal processes. Relaxation to thermal equilibrium is the most important dissipative process, being a key concept for the design of heat engines and refrigerators, contributing to the study of foundational questions of thermodynamics, and being relevant for quantum computing through the process of algorithmic cooling. Despite the importance of this kind of processes, their dynamics are far from being understood. We show that the free relaxation to thermal equilibrium follows intrinsically different paths depending on whether the temperature of the system increases (heating up) or decreases (cooling down), being faster in the first case. Our theory is exemplified using the recently developed thermal kinematics based on information geometry theory, utilizing three prototypical examples: a quantum two-level system, the quantum harmonic oscillator, and a trapped quantum Brownian particle, including both analytic results and numerical simulations. For this, we have extended the thermal kinematic approach to open quantum systems. Additionally, we offer a simple theoretical explanation in the case of a two level system and a more general picture for the other two systems based on the spectral decomposition of the Liouvillian and the spectral gap of reciprocal processes., Comment: 16 pages, 7 figures

The possibility of efficiently converting heat into work at the microscale has triggered an intense research effort to understand quantum heat engines, driven by the hope of quantum superiority over classical counterparts. In this work, we introduce a model featuring an atom-doped optical quantum cavity propelling a classical piston through radiation pressure. The model, based on the Jaynes-Cummings Hamiltonian of quantum electrodynamics, demonstrates the generation of mechanical work through thermal energy injection. We establish the equivalence of the piston expansion work with Alicki's work definition, analytically for quasistatic transformations and numerically for finite time protocols. We further employ the model to construct quantum Otto and Carnot engines, comparing their performance in terms of energetics, work output, efficiency, and power under various conditions. This model thus provides a platform to extract useful work from an open quantum system to generate net motion, and sheds light on the quantum concepts of work and heat., Comment: Updated version. 15 pages, 8 figures

We present extensive simulations of a quantum version of the Hopfield Neural Network to explore its emergent behavior. The system is a network of $N$ qubits oscillating at a given $\Omega$ frequency and which are coupled via Lindblad jump operators built with local fields $h_i$ depending on some given stored patterns. Our simulations show the emergence of pattern-antipattern oscillations of the overlaps with the stored patterns similar (for large $\Omega$ and small temperature) to those reported within a recent mean-field description of such a system, and which are originated deterministically by the quantum term including $s_x^i$ qubit operators. However, in simulations we observe that such oscillations are stochastic due to the interplay between noise and the inherent metastability of the pattern attractors induced by quantum oscillations, and then are damped in finite systems when one averages over many quantum trajectories. In addition, we report the system behavior for large number of stored patterns at the lowest temperature we can reach in simulations (namely $T=0.005\, T_C$). Our study reveals that for small-size systems the quantum term of the Hamiltonian has a negative effect on storage capacity, decreasing the overlap with the starting memory pattern for increased values of $\Omega$ and number of stored patterns. However, it also impedes the system to be trapped for long time in mixtures and spin-glass states. Interestingly, the system also presents a range of $\Omega$ values for which, although the initial pattern is destabilized due to quantum oscillations, other patterns can be retrieved and remain stable even for many stored patterns, implying a quantum-dependent nonlinear relationship between the recall process and the number of stored patterns.

Symmetries in an open quantum system lead to degenerated Liouvillian that physically implies the existence of multiple steady states. In such cases, obtaining the initial condition independent stead states is highly nontrivial since any linear combination of the \emph{true} asymptotic states, which may not necessarily be a density matrix, is also a valid asymptote for the Liouvillian. Thus, in this work we consider different approaches to obtain the \emph{true} steady states of a degenerated Liouvillian. In the ideal scenario, when the open system symmetry operators are known we show how these can be used to obtain the invariant subspaces of the Liouvillian and hence the steady states. We then discuss two other approaches that do not require any knowledge of the symmetry operators. These could be a powerful tool to deal with quantum many-body complex open systems. The first approach which is based on Gramm-Schmidt orthonormalization of density matrices allows us to obtain \emph{all} the steady states, whereas the second one based on large deviations allows us to obtain the non-degenerated maximum and minimum current-carrying states. We discuss our method with the help of an open para-Benzene ring and examine interesting scenarios such as the dynamical restoration of Hamiltonian symmetries in the long-time limit and apply the method to study the eigenspacing statistics of the nonequilibrium steady state., Comment: 11 pages and 4 figures

Automatic bill classification is an attractive task with many potential applications such as automated detection and counting in images or videos. To address this purpose we present a Deep Learning Model to classify Chilean Banknotes, because of its successful results in image processing applications. For optimal performance of the proposed model, data augmentation techniques are introduced due to the limited number of image samples. Positive results were achieved in this work, verifying that it could be a stating point to be extended to more complex applications., Comment: 3 pages, 3 figures, Posters Content EVIC 2019

We study the effect of an applied magnetic field on the nonequilibrium transport properties of a general cubic quantum network described by a tight-binding Hamiltonian with specially designed couplings to the leads that preserve open-system symmetries. We demonstrate that the symmetry of open systems can be manipulated by the direction of the magnetic field. Starting with all the symmetries preserved in absence of a field, the anisotropic and isotropic fields systematically break the symmetries, influencing all nonequilibrium properties. For simple cubic systems, we are able to identify the steady states that comprise of pure states, bath-dependent states (nonequilibrium steady states), and also nonphysical states. As an application, we show numerically for large cubic networks that the symmetry breaking can control nonequilibrium currents and that different environmental interactions can lead to novel features which can be engineered in artificial super-lattices and cold atoms., Comment: 18 pages, 7 figures, 2 appendixes. Videoabstract at the publishers webpage https://iopscience.iop.org/article/10.1088/1367-2630/aba0e4/meta

The theory of open quantum system is one of the most essential tools for the development of quantum technologies. Furthermore, the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) Master Equation plays a key role as it is the most general generator of Markovian dynamics in quantum systems. In this paper, we present this equation together with its derivation and methods of resolution. The presentation tries to be as self-contained and straightforward as possible to be useful to readers with no previous knowledge of this field., Comment: Pedagogical paper, aimed to people which knowledge about quantum mechanics but not previous background about quantum master equations

Symmetries play a crucial role in ubiquitous systems found in Nature. In this work, we propose an elegant approach to detect symmetries by measuring quantum currents. Our detection scheme relies on initiating the system in an anti-symmetric initial condition, with respect to the symmetric sites, and using a probe that acts like a local noise. Depending on the position of the probe the currents exhibit unique signatures such as a quasi-stationary plateau indicating the presence of meta-stability and multi-exponential decays in case of multiple symmetries. The signatures are sensitive to the probe and vanish completely when the timescale of the coherent system dynamics is much longer than the timescale of the probe. These results are demonstrated using a $4$-site model and an archetypal example of the para-benzene ring and are shown to be robust under a weak disorder., Comment: 10 pages + 3 page supplementary material. Comments are welcome

We propose a simple diatomic system trapped inside an optical cavity to control the energy flow between two thermal baths. Through the action of the baths the system is driven to a non- equilibrium steady state. Using the Large Deviation theory we show that the number of photons flowing between the two baths is dramatically different depending on the symmetry of the atomic states. Here we present a deterministic scheme to prepare symmetric and antisymmetric atomic states with the use of external driving fields, thus implementing an atomic control switch for the energy flow., Comment: 8 pages, 3 figures

We prove analytically that both fermionic and bosonic uniform d-dimensional lattices can be reduced to a set of independent one-dimensional modes. This reduction leads to the conclusion that the dynamics in uniform fermionic and bosonic lattices is always ballistic. By the use of the Jordan-Wigner transformation we extend our analysis to spin lattices, proving the existence of both ballistic and non-ballistic subspaces in any dimension and for any system size. We then relate the nature of transport with the number of excitations in the spin lattice, indicating that a single excitation propagates always ballistically and that the non-ballistic behavior of uniform spin lattices is a consequence of the interaction between different excitations., Comment: 13 pages, 5 figures

Probability Theory and Statistics are two of the most useful mathematical fields, and also two of the most difficult to learn. In other science fields, as Physics, experimentation is an useful tool to develop students intuition, but the application of this tool to Statistics is much more difficult. In this paper we show how Monte Carlo techniques can be used to perform numerical experiments, by the use of pseudorandom numbers, and how these experiments can help to the understanding of Statistics and Physics. Monte Carlo techniques are broadly used in scientific research, but they are learnt usually in very specific curses of higher education. By the use of computer simulation these techniques can also be taught at elementary school and they can help to understand and visualise concepts as variance, mean or a probability distribution function. Finally, the use of new technologies, as Javascript and HTML is discussed., Comment: Text in Spanish, 7 pages, 3 figures, Presented in the conference "Jornadas Virtuales en Did\'actica de la Estad\'istica, Probabilidad y Combinatoria", Granada, Spain (2013)

Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and statistics in open quantum systems. Such control is enabled by a first-order-type dynamic phase transition in current statistics and the associated coexistence of different transport channels (or nonequilibrium steady states) classified by symmetry. Microreversibility then ensues, via the Gallavotti-Cohen fluctuation theorem, a twin dynamic phase transition for rare current fluctuations. Interestingly, the symmetry present in the initial state is spontaneously broken at the fluctuating level, where the quantum system selects the symmetry sector that maximally facilitates a given fluctuation. We illustrate these results in a qubit network model motivated by the problem of coherent energy harvesting in photosynthetic complexes, and introduce the concept of a symmetry-controlled quantum thermal switch, suggesting symmetry-based design strategies for quantum devices with controllable transport properties., Comment: 12 pages, 6 figures

It has been proved by Kempe that discrete quantum walks on the hypercube (HC) hit exponentially faster than the classical analog. The same was also observed numerically by Krovi and Brun for a slightly different property, namely, the expected hitting time. Yet, to what extent this striking result survives in more general graphs, is to date an open question. Here we tackle this question by studying the expected hitting time for quantum walks on HCs that are embedded into larger symmetric structures. By performing numerical simulations of the discrete quantum walk and deriving a general expression for the classical hitting time, we observe an exponentially increasing gap between the expected classical and quantum hitting times, not only for walks on the bare HC, but also for a large family of embedded HCs. This suggests that the quantum speedup is stable with respect to such embeddings., Comment: 21 pages, 10 figures

We study the model of projective simulation (PS), a novel approach to artificial intelligence based on stochastic processing of episodic memory which was recently introduced [H.J. Briegel and G. De las Cuevas. Sci. Rep. 2, 400, (2012)]. Here we provide a detailed analysis of the model and examine its performance, including its achievable efficiency, its learning times and the way both properties scale with the problems' dimension. In addition, we situate the PS agent in different learning scenarios, and study its learning abilities. A variety of new scenarios are being considered, thereby demonstrating the model's flexibility. Furthermore, to put the PS scheme in context, we compare its performance with those of Q-learning and learning classifier systems, two popular models in the field of reinforcement learning. It is shown that PS is a competitive artificial intelligence model of unique properties and strengths., Comment: Accepted for publication in New Generation Computing. 23 pages, 23 figures

Recently, several works have analysed the efficiency of photosynthetic complexes in a transient scenario and how that efficiency is affected by environmental noise. Here, following a quantum master equation approach, we study the energy and excitation transport in fully connected networks both in general and in the particular case of the Fenna-Matthew-Olson complex. The analysis is carried out for the steady state of the system where the excitation energy is constantly "flowing" through the system. Steady state transport scenarios are particularly relevant if the evolution of the quantum system is not conditioned on the arrival of individual excitations. By adding dephasing to the system, we analyse the possibility of noise-enhancement of the quantum transport., Comment: 10 pages, single column, 6 figures. Accepted for publication in Plos One

We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. Implications of these results on energy transfer in biological light harvesting systems, and the role of quantum coherences and entanglement are discussed., Comment: 6 pages, 4 figures

The Fisher-Shannon statistical measure of complexity is analyzed for a continuous manifold of quantum observables. It is probed then than calculating it only in the configuration and momentum spaces will not give a complete description for certain systems. Then a more general measure for the complexity of a quantum system by the integration of the usual Fisher-Shannon measure over all the parameter space is proposed. Finally, these measures are applied to the concrete case of a free particle in a box., Comment: 6 pages, 5 figures. Published version

This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the proposal and analysis of a new set of measures of spreading for orthogonal polynomials, to quantum computation and learning devices and to the analysis of entanglement in systems of identical fermions, in this field we propose a separability criteria for pure states of N identical fermions and the entanglement of two-electron atoms is studied, a new separability criteria for continuous variable systems is also analyzed. The notions of information, complexity and entanglement play a central role., Comment: Phd Thesis of Daniel Manzano, directed by Jes\'us S\'anchez-Dehesa and \'Angel Ricardo Plastino. All it is in English except the legal texts, acknowledgments and the introduction that are in Spanish. Defended at the University of Granada, April 12, 2010

The Fisher-Shannon complexity is used to quantitatively estimate the contribution of relativistic effects to on the internal disorder of Klein-Gordon single-particle Coulomb systems which is manifest in the rich variety of three-dimensional geometries of its corresponding quantum-mechanical probability density. It is observed that, contrary to the non-relativistic case, the Fisher-Shannon complexity of these relativistic systems does depend on the potential strength (nuclear charge). This is numerically illustrated for pionic atoms. Moreover, its variation with the quantum numbers (n, l, m) is analysed in various ground and excited states. It is found that the relativistic effects enhance when n and/or l are decreasing., Comment: 4 pages, 3 figures, Accepted in EPL (Europhysics Letters)

The internal disorder of a D-dimensional hydrogenic system, which is strongly associated to the non-uniformity of the quantum-mechanical density of its physical states, is investigated by means of the shape complexity in the two reciprocal spaces. This quantity, which is the product of the disequilibrium and the Shannon entropic power, is mathematically expressed for both ground and excited stationary states in terms of certain entropic functionals of Laguerre and Gegenbauer (or ultraspherical) polynomials. Emphasis is made in the ground and circular states., Comment: 12 pages, 0 figures. Published in Mathematical Physics and Field Theory

We consider quantum learning machines -- quantum computers that modify themselves in order to improve their performance in some way -- that are trained to perform certain classical task, i.e. to execute a function which takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machine in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the k-th root of NOT (NOT = logical negation), with k=2^m and m \in N. The reason for this speed-up is that classical machine requires memory of size log k=m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k., Comment: 4 pages, 4 figures