Search

We investigate the use of Quantum Neural Networks for discovering and implementing quantum error-correcting codes. Our research showcases the efficacy of Quantum Neural Networks through the successful implementation of the Bit-Flip quantum error-correcting code using a Quantum Autoencoder, effectively correcting bit-flip errors in arbitrary logical qubit states. Additionally, we employ Quantum Neural Networks to restore states impacted by Amplitude Damping by utilizing an approximative 4-qubit error-correcting codeword. Our models required modification to the initially proposed Quantum Neural Network structure to avoid barren plateaus of the cost function and improve training time. Moreover, we propose a strategy that leverages Quantum Neural Networks to discover new encryption protocols tailored for specific quantum channels. This is exemplified by learning to generate logical qubits explicitly for the bit-flip channel. Our modified Quantum Neural Networks consistently outperformed the standard implementations across all tasks.

We theoretically demonstrated the possible emergence of slow-light self-induced transparency solitons in the infinite one-dimensional coupled cavity array, with each cavity containing a single qubit. We have predicted a substantial dependence of pulse transparency on its dimensionless width $\tau_0$. In particular, short pulses whose widths range from $\tau_0\ll 1$ to $\tau_0\lesssim 1$ exhibit simple, almost linear dispersion law with a finite frequency gap of the order of the cavity array photonic band gap. That is, the medium is opaque for very short pulses with carrier wave frequency below the photonic gap. When the pulse width exceeds the critical one, a twin transparency window separated by a finite band gap appears in the soliton pulse dispersion law. Observation of predicted effects within the proposed setup would be of interest for understanding the properties of self-induced transparency effect in general and future applications in the design of quantum technological devices.

Artificial intelligence in the form of deep learning is now very popular and directly implemented in many areas of science and technology. In the present work we study time evolution of Discrete Breathers in one-dimensional nonlinear chains using the framework of Convolutional Neural Networks. We focus on differentiating discrete breathers which are localized nonlinear modes from linearized phonon modes. The breathers are localized in space and time-periodic solutions of non-linear discrete lattices while phonons are the linear collective oscillations of interacting atoms and molecules. We show that deep learning neural networks are indeed able not only to distinguish breather from phonon modes but also determine with high accuracy the underlying nonlinear on-site potentials that generate breathers. This work can have extensions to more complex natural systems.

In quantum targeted energy transfer, bosons are transferred from a certain crystal site to an alternative one, utilizing a nonlinear resonance configuration similar to the classical targeted energy transfer. We use a novel computational method based on machine learning algorithms in order to investigate selectivity as well as efficiency of the quantum transfer in the context of a dimer and a trimer system. We find that our method identifies resonant quantum transfer paths that allow boson transfer in unison. The method is readily extensible to larger lattice systems involving nonlinear resonances., Comment: REVTeX 4.2, 9 pages, 7 figures

We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space dimension of each system and thus determines the minimal number of nodes necessary to capture the essential information contained in the chaotic time series. The constructed chaotic autoencoders generate similar maximal Lyapunov exponents as the original chaotic systems and thus encompass their essential dynamical information.

The spread of COVID-19 during the initial phase of the first half of 2020 was curtailed to a larger or lesser extent through measures of social distancing imposed by most countries. In this work, we link directly, through machine learning techniques, infection data at a country level to a single number that signifies social distancing effectiveness. We assume that the standard SIR model gives a reasonable description of the dynamics of spreading, and thus the social distancing aspect can be modeled through time-dependent infection rates that are imposed externally. We use an exponential ansatz to analyze the SIR model, find an exact solution for the time-independent infection rate, and derive a simple first-order differential equation for the time-dependent infection rate as a function of the infected population. Using infected number data from the "first wave" of the infection from eight countries, and through physics-informed machine learning, we extract the degree of linear dependence in social distancing that led to the specific infections. We find that in the two extremes are Greece, with the highest decay slope on one side, and the US on the other with a practically flat "decay". The hierarchy of slopes is compatible with the effectiveness of the pandemic containment in each country. Finally, we train our network with data after the end of the analyzed period, and we make week-long predictions for the current phase of the infection that appear to be very close to the actual infection values.

The conditions leading to flat dispersionless frequency bands in truly one-dimensional parity-time ($\cal PT$) symmetric metamaterials comprising split-ring resonators (SRRs) arranged in a binary pattern are obtained analytically. In this paradigmatic system, in which the SRRs are coupled through both electric and magnetic dipole-dipole forces, flat-bands may arise from tailoring its natural parameters (such as, e.g., the coupling coefficients between SRRs) and not from geometrical effects. For sets of parameters which values are tailored to flatten the upper band of the spectrum, the solution of the corresponding quadratic eigenvalue problem reveals the existence of compact, two-site localized eigenmodes. Numerical simulations confirm the existence and the dynamic stability of such modes, which can be formed through the evolution of single-site initial excitations without disorder or nonlinearity., Comment: to be published in Scientific Reports (2019)

We address light propagation properties in complex media consisting of random distributions of lenses that have specific focusing properties. We present both analytical and numerical techniques that can be used to study emergent properties of light organization in these media. As light propagates, it experiences multiple scattering leading to the formation of light bundles in the form of branches; these are random yet occur systematically in the the medium, particularly in the weak scattering limit. On the other hand, in the strong scattering limit we find that coalescence of branches may lead to the formation of extreme waves of the "rogue wave" type. These waves appear at specific locations and arise in the linear as well as in the nonlinear regimes. We present both the weak and strong scattering limit and show that these complex phenomena can be studied numerically and analytically through simple models., This is a Chapter from the book: Quodons in Mica: Nonlinear localized traveling excitations in crystals. Springer Series in Materials Science

Surface plasmon polaritons (SPPs) are coherent electromagnetic surface waves trapped on an insulator-conductor interface. The SPPs decay exponentially along the propagation due to conductor losses, restricting the SPPs propagation length to few microns. Gain materials can be used to counterbalance the aforementioned losses. We provide an exact expression for the gain, in terms of the optical properties of the interface, for which the losses are eliminated. In addition, we show that systems characterized by lossless SPP propagation are related to PT symmetric systems. Furthermore, we derive an analytical critical value of the gain describing a phase transition between lossless and prohibited SPPs propagation. The regime of the aforementioned propagation can be directed by the optical properties of the system under scrutiny. Finally, we perform COMSOL simulations verifying the theoretical findings.

Nonequilibrium, quasi-stationary states of a one-dimensional "hard" $\phi^4$ deterministic lattice, initially thermalized to a particular temperature, are investigated when brought into contact with a stochastic thermal bath at lower temperature. For lattice initial temperatures sufficiently higher than those of the bath, energy localization through the formation of nonlinear excitations of the breather type during the cooling process occurs. These breathers keep the nonlinear lattice away from thermal equilibrium for relatively long times. In the course of time some breathers are destroyed by fluctuations, allowing thus the lattice to reach another nonequilibrium state of lower energy. The number of breathers thus reduces in time; the last remaining breather, however, exhibits amazingly long life-time demonstrated by extensive numerical simulations using a quasi-symplectic integration algorithm. For the single-breather states we have calculated the lattice velocity distribution unveiling non-gaussian features describable in a closed functional form. Moreover, the influence of the coupling constant on the life-time of a single breather has been explored. The latter exhibits power-law behaviour as the coupling constant approaches the anticontinuous limit., Comment: 5 pages, 10 figures

${\mathcal PT}-$symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime are investigated: a system of coupled classical oscillators, and a Schr\"{o}dinger dimer representing the coupling of field amplitudes; each system representing a wide class of physical models. Through a thorough analysis of their stability behaviour, we find that turning on the coupling parameter in the classical dimer system, leads initially to decreased stability but then to re-entrant transitions from the exact to the broken ${\mathcal PT}-$phase and vice versa, as it is increased beyond a critical value. On the other hand, the Schr\"{o}dinger dimer behaves more like a single oscillator with time-periodic gain/loss. In addition, we are able to identify the conditions under which the behaviour of the two dimer systems coincides and/or reduces to that of a single oscillator., Comment: 9 pages, 9 figures, META14 Conference, subm. Special Issue Appl. Phys. A

The spatiotemporal complexity induced by perturbed initial excitations through the development of modulational instability in nonlinear lattices with or without disorder, may lead to the formation of very high amplitude, localized transient structures that can be named as extreme events. We analyze the statistics of the appearance of these collective events in two different universal lattice models; a one-dimensional nonlinear model that interpolates between the integrable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schr\"odinger (DNLS) equation, and a two-dimensional disordered DNLS equation. In both cases, extreme events arise in the form of discrete rogue waves as a result of nonlinear interaction and rapid coalescence between mobile discrete breathers. In the former model, we find power-law dependence of the wave amplitude distribution and significant probability for the appearance of extreme events close to the integrable limit. In the latter model, more importantly, we find a transition in the the return time probability of extreme events from exponential to power-law regime. Weak nonlinearity and moderate levels of disorder, corresponding to weak chaos regime, favour the appearance of extreme events in that case., Comment: Invited Chapter in a Special Volume, World Scientific. 19 pages, 9 figures

We present numerical simulations for the propagation of surface plasmon polaritons in a dielectric-metal-dielectric waveguide using COMSOL multiphysics software. We show that the use of an active dielectric with gain that compensates metal absorption losses enhances substantially plasmon propagation. Furthermore, the introduction of the active material induces, for a specific gain value, a root in the imaginary part of the propagation constant leading to infinite propagation of the surface plasmon. The computational approaches analyzed in this work can be used to define and tune the optimal conditions for surface plasmon polariton amplification and propagation.

A one dimensional, parity-time (${\cal PT}$)-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken ${\cal PT}$-phase is determined through the calculation of the eigenfrequency spectrum for two different configurations; the one with equidistant split-rings and the other with the split-rings forming a binary pattern (${\cal PT}$ dimer chain). The latter system features a two-band, gapped spectrum with its shape determined by the gain/loss coefficient as well as the inter-element coupling. In the presense of nonlinearity, the ${\cal PT}$ dimer chain with balanced gain and loss supports nonlinear localized modes in the form of novel discrete breathers below the lower branch of the linear spectrum. These breathers, that can be excited from a weak applied magnetic field by frequency chirping, can be subsequently driven solely by the gain for very long times. The effect of a small imbalance between gain and loss is also considered. Fundamendal gain-driven breathers occupy both sites of a dimer, while their energy is almost equally partitioned between the two split-rings, the one with gain and the other with loss. We also introduce a model equation for the investigation of classical ${\cal PT}$ symmetry in zero dimensions, realized by a simple harmonic oscillator with matched time-dependent gain and loss that exhibits a transition from oscillatory to diverging motion. This behaviour is similar to a transition from the exact to the broken ${\cal PT}$ phase in higher-dimensional ${\cal PT}-$ symmetric systems. A stability condition relating the parameters of the problem is obtained in the case of piecewise constant gain/loss function that allows for the construction of a phase diagram with alternating stable and unstable regions., Comment: 10 pages, 11 figs, subm. to Applied Physics A for the Proceedings of the META13 Conference

We investigate dynamical aspects of the discrete nonlinear Schr��dinger equation (DNLS) in finite lattices. Starting from a periodic chain with nearest neighbor interactions, we insert randomly links connecting distant pairs of sites across the lattice. Using localized initial conditions we focus on the time averaged probability of occupation of the initial site as a function of the degree of complexity of the lattice and nonlinearity. We observe that selftrapping occurs at increasingly larger values of the nonlinearity parameter as the lattice connectivity increases, while close to the fully coupled network limit, localization becomes more preferred. For nonlinearity values above a certain threshold we find a reentrant localization transition, viz. localization when the number of long distant bonds is small followed by delocalization and enhanced transport at intermediate bond numbers while close to the fully connected limit localization reappears., 5 pages, 5 figures

The existence and stability of dissipative discrete breathers (DDBs) in rf superconducting quantum interference device (SQUID) arrays in both one and two dimensions is investigated numerically. In an rf SQUID array, the nonlinearity which is intrinsic to each SQUID due to the presence of the Josephson junction (on-site nonlinearity), along with the weak coupling of each SQUID to its nearest neighbors through magnetic forces, result in the appearance of discrete breathers. We analyze several discrete breather excitations, both in one and two dimensions, which are subjected to unavoidable losses. These losses, however, are counter-balanced by an external flux source leading to linearly stable discrete breather structures up to relatively large coupling parameters. We show that DDB excitations may locally alter the magnetic response of array from paramagnetic to diamagnetic or vice versa, and that they are not destroyed by increasing the dimensionality., 9 pages, 13 figures, submitted to Nonlinear Phenomena in Complex Systems

The existence and stability of discrete breathers (DBs) in one-dimensional and two-dimensional magnetic metamaterials (MMs), which consist of periodic arrangem ents (arrays) of split-ring resonators (SRRs), is investigated numerically. We consider different configurations of the SRR arrays, which are related to the relative orientation of the SRRs in the MM, both in one and two spatial dimensions. In the latter case we also consider anisotropic MMs. Using standard numerical methods we construct several types of linearly stable breather excitations both in Hamiltonian and dissipative MMs (dissipative breathers). The study of stability in both cases is performed using standard Floquet analysi s. In both cases we found that the increase of dimensionality from one to two spatial dimensions does not destroy the DBs, which may also exist in the case of moderate anisotropy (in two dimensions). In dissipative MMs, the dynamics is governed by a power balance between the mainly Ohmic dissipation and driving by an alternating magnetic field. In that case it is demonstrated that DB excitation locally alters the magnetic response of MMs from paramagnetic to diamagnetic. Moreover, when the frequency of the applied field approaches the SRR resonance frequency, the magnetic response of the MM in the region of the DB excitation may even become negative (extreme diamagnetic)., Comment: 12 pages 15 figures

An rf superconducting quantum interference device (SQUID) array in an alternating magnetic field is investigated with respect to its effective magnetic permeability, within the effective medium approximation. This system acts as an inherently nonlinear magnetic metamaterial, leading to negative magnetic response, and thus negative permeability, above the resonance frequency of the individual SQUIDs. Moreover, the permeability exhibits oscillatory behavior at low field intensities, allowing its tuning by a slight change of the intensity of the applied field., Comment: 3 pages, 4 figures, accepted by Applied Physics Letters, in production

We study the thermodynamics of discrete breathers by transforming a lattice of weakly coupled nonlinear oscillators into an effective Ising pseudospin model. We introduce a replica ensemble and investigate the effective system susceptibilities through the replica overlap distribution. We find that a transition occurs at a given temperature to a new phase characterized by a slow decay of the relevant correlation functions. Comparison of long time pseudospin correlation functions to maximal replica overlap demonstrates that the high temperature phase has glassy-like properties induced by short range order found in the system., Comment: 19 pages, 6 figures

We study the dynamics of the discrete nonlinear Schr{��}dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this {\em non-Gibbsian} state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather.

Two headed motor proteins, such as kinesin and dynein, hidrolyze environmental ATP in order to propel unidirectionally along cytoskeletal filaments such as microtubules. In the case of kinesin, protein heads bind primarily on the alpha tubulin site of asymmetric alpha-beta 8nm-long tubulin dimers that constitute the microtubular protofilaments. Kinesin dimers overcome local binding forces up to 5pN and are known to move on protofilaments with ATP concentration-dependent speeds while hydrolizing on average one ATP molecule per 8nm step. The salient features of protein trajectories are the distinct abrupt usually 8nm-long steps from one tubulin dimer to the next interlaced with long quiescent binding periods at a tubulin site. Discrete walks of this type are characterized by substantially reduced variances compared to pure biased random walks, and as a result rule out flashing-type ratchet models as possible mechanisms for motor movement. On the other hand, simple additive correlated brownian ratchets that present exactly these discrete trajectory patterns with reduced variances are compatible with the general features of protein motion. In the simplest such model the protein is simplified to a single particle moving in a periodic non-symmetric tubulin-derived potential and the environmental and ATP interaction is included in a correlated additive noise term. For this model we show that the resulting protein walk has features resembling experimental data. Furthermore, in more realistic mechanical models of two masses connected by a spring we find qualitative agreement with recent experimental facts related to motion of protein chimaeras formed through kinesin motor domains with non-claret disjunctional (ncd) neck regions., To appear in Advances in Structural Biology (Special Issue)

We study numerically the evolution of wavepackets in quasi one-dimensional random systems described by a tight-binding Hamiltonian with long-range random interactions. Results are presented for the scaling properties of the width of packets in three time regimes: ballistic, diffusive and localized. Particular attention is given to the fluctuations of packet widths in both the diffusive and localized regime. Scaling properties of the steady-state distribution are also analyzed and compared with theoretical expression borrowed from one-dimensional Anderson theory. Analogies and differences with the kicked rotator model and the one-dimensional localization are discussed., 32 pages, LaTex, 11 PostScript figures

We study scaling properties of the localized eigenstates of the random dimer model in which pairs of local site energies are assigned at random in a one dimensional disordered tight-binding model. We use both the transfer matrix method and the direct diagonalization of the Hamiltonian in order to find how the localization length of a finite sample scales to the localization length of the infinite system. We derive the scaling law for the localization length and show it to be related to scaling behavior typical of uncorrelated Band Random Matrix, Anderson and Lloyd models., 17 pages in Latex and 7 Postscript figures