Related papers: Unsupervised Techniques to Detect Quantum Chaos
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
Symmetry in biological and physical systems is a product of self organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry based feature extrac-tion or representation by neural networks may unravel the…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
Choosing a meaningful subset of features from high-dimensional observations in unsupervised settings can greatly enhance the accuracy of downstream analysis, such as clustering or dimensionality reduction, and provide valuable insights into…
Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to…
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…
It was recently shown (quant-ph/9909074) that parasitic random interactions between the qubits in a quantum computer can induce quantum chaos and put into question the operability of a quantum computer. In this work I investigate whether…
The quantization error in a fixed-size Self-Organizing Map (SOM) with unsupervised winner-take-all learning has previously been used successfully to detect, in minimal computation time, highly meaningful changes across images in medical…
For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…
We study the properties of spectra and eigenfunctions for a chain of $1/2- $spins (qubits) in an external time-dependent magnetic field, and under the conditions of non-selective excitation (when the amplitude of the magnetic field is…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos,…
Parametric correlations of energy spectra of quantum chaotic systems are presented in the orthogonal-unitary and symplectic-unitary crossover region. The spectra are allowed to disperse as a function of two external perturbations: one of…
We remind the reader that it is possible to tell if two or more eigenvalues of a matrix are equal, without calculating the eigenvalues. We then use this property to detect (avoided) crossings in the spectra of quantum Hamiltonians…
Chaotic maps are very important for establishing chaos-based image encryption systems. This paper introduces a coupling chaotic system based on a certain unit transform, which can combine any two 1D chaotic maps to generate a new one with…
We investigate universal features of measurement-and-feedback control of quantum chaotic dynamics by examining the quantum Arnold cat map, a paradigmatic model of quantum chaos. Inspired by probabilistic control of classical chaos, our…
This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary…
We investigate circuit complexity to characterize chaos in multiparticle quantum systems. In the process, we take a stride to analyze open quantum systems by using complexity. We propose a new diagnostic of quantum chaos from complexity…