Quantum inspired approach for denoising with application to medical imaging.

Background noise in many fields such as medical imaging poses significant challenges for accurate diagnosis, prompting the development of denoising algorithms. Traditional methodologies, however, often struggle to address the complexities of noisy environments in high dimensional imaging systems. This paper introduces a novel quantum-inspired approach for image denoising, drawing upon principles of quantum and condensed matter physics.

Quantum inspired approach for denoising with application to medical imaging.

Background noise in many fields such as medical imaging poses significant challenges for accurate diagnosis, prompting the development of denoising algorithms. Traditional methodologies, however, often struggle to address the complexities of noisy environments in high dimensional imaging systems. This paper introduces a novel quantum-inspired approach for image denoising, drawing upon principles of quantum and condensed matter physics.

Chaos-Assisted Long-Range Tunneling for Quantum Simulation.

We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with chaos-induced long-range hoppings t_{n}∝1/n between sites at a distance n. We provide a numerical demonstration of the robustness of the results and derive an analytical prediction for the hopping term law.

Accuracy of neural networks for the simulation of chaotic dynamics: Precision of training data vs precision of the algorithm.

We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural network techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural network techniques adapted to time series, namely, reservoir computing [using Echo State Network (ESN)], long short-term memory, and temporal convolutional network, for both short- and long-time predictions, and assess their efficiency and accuracy. Our results show that the ESN network is better at predicting accurately the dynamics of the system, and that in all cases, the precision of the algorithm is more important than the precision of the training data for the accuracy of the predictions.

Chaos-assisted tunneling resonances in a synthetic Floquet superlattice.

The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to the all-purpose quantum computer. So far, most efforts in this domain have been directed to either fully regular or fully chaotic systems. Here, we focus on the intermediate regime, where regular orbits are surrounded by a large sea of chaotic trajectories.

Multifractality of open quantum systems.

We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify the relationship between the eigenstates and the classical structures, and we quantify their multifractality at different scales. Based on this study, we conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but these states are multifractal instead of ergodic at each level of the hierarchy.

Chaos-assisted tunneling in the presence of Anderson localization.

Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate. Here we study chaos-assisted tunneling in the presence of Anderson localization effects in the chaotic sea.

Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality.

We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1 View Article and Find Full Text PDF

Basin entropy: a new tool to analyze uncertainty in dynamical systems.

In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules.

Multifractality of quantum wave functions in the presence of perturbations.

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model, and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations.

Two scenarios for quantum multifractality breakdown.

We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value.

Multifractality of quantum wave packets.

We study a version of the mathematical Ruijsenaars-Schneider model and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, which is different from the multifractality of eigenvectors but related to it, as is the rate of the decrease.

Optically guided beam splitter for propagating matter waves.

We study experimentally and theoretically a beam splitter setup for guided atomic matter waves. The matter wave is a guided atom laser that can be tuned from quasimonomode to a regime where many transverse modes are populated, and propagates in a horizontal dipole beam until it crosses another horizontal beam at 45°. We show that depending on the parameters of this X configuration, the atoms can all end up in one of the two beams (the system behaves as a perfect guide switch), or be split between the four available channels (the system behaves as a beam splitter).

Exploring classically chaotic potentials with a matter wave quantum probe.

We study an experimental setup in which a quantum probe, provided by a quasimonomode guided atom laser, interacts with a static localized attractive potential whose characteristic parameters are tunable. In this system, classical mechanics predicts a transition from regular to chaotic behavior as a result of the coupling between the different degrees of freedom. Our experimental results display a clear signature of this transition.

Regular modes in rotating stars.

Despite more and more observational data, stellar acoustic oscillation modes are not well understood as soon as rotation cannot be treated perturbatively. In a way similar to semiclassical theory in quantum physics, we use acoustic ray dynamics to build an asymptotic theory for the subset of regular modes which are the easiest to observe and identify. Comparisons with 2D numerical simulations of oscillations in polytropic stars show that both the frequency and amplitude distributions of these modes can accurately be described by an asymptotic theory for almost all rotation rates.

Multifractal wave functions of simple quantum maps.

We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting and wavelet methods). We compare the results of the two methods over a wide range of values.

Quantum algorithm for exact Monte Carlo sampling.

We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact Monte Carlo sampling methods, and yields a polynomial gain compared to classical procedures.

Chirality of triangular antiferromagnetic clusters as a qubit.

We show that the chirality of triangular antiferromagnetic clusters can be used as a qubit even if it is entirely decoupled from the total spin of the cluster. In particular, we estimate the orbital moment associated with the chirality, and we show that it can be large enough to allow a direct measurement of the chirality with a field perpendicular to the cluster. Consequences for molecular magnets are discussed, and an alternative implementation with Cu atoms on a surface is proposed, for which one- and two-qubit gates are worked out in detail.

Spectral properties of the Google matrix of the World Wide Web and other directed networks.

We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure in the vicinity of the maximal eigenvalue for Google damping parameter α equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to another, reflecting specific properties of the networks.

Delocalization transition for the Google matrix.

We study the localization properties of eigenvectors of the Google matrix, generated both from the world wide web and from the Albert-Barabási model of networks. We establish the emergence of a delocalization phase for the PageRank vector when network parameters are changed. For networks with localized PageRank, eigenvalues of the matrix in the complex plane with a modulus above a certain threshold correspond to localized eigenfunctions while eigenvalues below this threshold are associated with delocalized relaxation modes.

Chaotic dynamics of a Bose-Einstein condensate coupled to a qubit.

We study numerically the coupling between a qubit and a Bose-Einstein condensate (BEC) moving in a kicked optical lattice using Gross-Pitaevskii equation. In the regime where the BEC size is smaller than the lattice period, the chaotic dynamics of the BEC is effectively controlled by the qubit state. The feedback effects of the nonlinear chaotic BEC dynamics preserve the coherence and purity of the qubit in the regime of strong BEC nonlinearity.

Time reversal of Bose-Einstein condensates.

Using Gross-Pitaevskii equation, we study the time reversibility of Bose-Einstein condensates (BEC) in kicked optical lattices, showing that in the regime of quantum chaos, the dynamics can be inverted from explosion to collapse. The accuracy of time reversal decreases with the increase of atom interactions in BEC, until it is completely lost. Surprisingly, quantum chaos helps to restore time reversibility.

Wave chaos in rapidly rotating stars.

The effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens fresh perspectives for rapidly rotating star seismology and also provides a potentially observable manifestation of wave chaos in a large-scale natural system.

Quantum computing of semiclassical formulas.

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.

Multifractality and intermediate statistics in quantum maps.

We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical computations and provide analytical arguments showing that the generalized fractal dimensions are directly related to the parameter of the underlying classical map, and thus to other properties such as spectral statistics. Our results could be relevant for Anderson and quantum Hall transitions, where wave functions also show multifractality.