Related papers: Chaos and complexity by design
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
Eigenlevel correlation diagrams has proven to be a very useful tool to understand eigenstate characteristics of classically chaotic systems. In particular, we showed in a previous publication [Phys. Rev. Lett. 80, 944 (1998)] how to unveil…
We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
Out-of-time-ordered correlators (OTOCs), defined via the squared commutator of a time-evolving and a stationary operator, represent observables that provide useful indicators for chaos and the scrambling of information in complex quantum…
Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos. Of the four operators involved, one pair may be regarded as a source and the other as a probe. A usual approach, applicable to large-$N$ systems such as the SYK…
The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the…
In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
The out-of-time ordered correlator (OTOC) is a measure of scrambling of quantum information. Scrambling is intuitively considered to be a significant feature of chaotic systems and thus the OTOC is widely used as a measure of chaos. For…
Out-of-time-ordered correlators (OTOC) are a quantifier of quantum information scrambling and quantum chaos. We propose an efficient quantum algorithm to measure OTOCs that provides an exponential speed-up over the best known classical…
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…
In classical dynamical systems, chaotic behavior is often associated with exponential sensitivity to initial conditions together with global phase-space structure. Translating this geometric concept to the strictly linear framework of…
We investigate measures of chaos in the measurement record of a quantum system which is being observed. Such measures are attractive because they can be directly connected to experiment. Two measures of chaos in the measurement record are…
We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…
We investigate a quantum algorithm which simulates efficiently the quantum kicked rotator model, a system which displays rich physical properties, and enables to study problems of quantum chaos, atomic physics and localization of electrons…
Mapping a complex network of $N$coupled identical oscillators to a quantum system, the nearest neighbor level spacing (NNLS) distribution is used to identify collective chaos in the corresponding classical dynamics on the complex network.…
We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the…