Related papers: Unravelling quantum chaos using persistent homolog…
In this paper, we develop a blended dynamics framework for open quantum networks with diffusive couplings. The network consists of qubits interconnected through Hamiltonian couplings, environmental dissipation, and consensus-like diffusive…
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data analysis. These filtrations quantify, in a forward direction,…
The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of non-equilibrium topological invariants is a central issue and usually necessitates the information of quantum…
Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…
We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…
We have revealed that the barrier-tunneling process in non-integrable systems is strongly linked to chaos in complex phase space by investigating a simple scattering map model. The semiclassical wavefunction reproduces complicated features…
I propose to study the complex physics of topological phases by an all optical implementation of a discrete-time quantum walk. The main novel ingredient is the use of parametric amplifiers in the random network which can in turn be used to…
Random dynamics in isolated quantum systems is of practical use in quantum information and is of theoretical interest in fundamental physics. Despite a large number of theoretical studies, it has not been addressed how random dynamics can…
In classical mechanics, driven systems with dissipation often exhibit complex, fractal dynamics known as strange attractors. This paper addresses the fundamental question of how such structures manifest in the quantum realm. We investigate…
We investigate quantum information processing and manipulations in disordered systems of ultracold atoms and trapped ions. First, we demonstrate generation of entanglement and local realization of quantum gates in a quantum spin glass…
Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper algorithm} and \emph{persistent homology}. In this paper we introduce new…
In driven-dissipative bosonic systems, the interplay between coherent driving, inter-particle interactions and dissipation leads to a rich variety of non-equilibrium stationary states (NESS). In the semiclassical limit, the flow topology of…
Qualitative methods such as the linear sampling method and the factorization method reconstruct acoustic scatterers through sampling indicators. In practice, these indicators are gray-scale fields on a prescribed sampling window and a…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…
Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly.…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
It has been recently realized that dissipative processes can be harnessed and exploited to the end of coherent quantum control and information processing. In this spirit we consider strongly dissipative quantum systems admitting a…