Related papers: A relation between Krylov and Nielsen complexity
We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
We study a periodically driven macrospin system with anisotropic long-range interactions and collective dissipation, described by a Lindblad master equation. In the thermodynamic limit ($N\to\infty$), a mean-field treatment yields classical…
In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly,…
In the studies of the squeezing it is customary to focus more attention on the particular squeezed states and their evolution than on the dynamical operations that could squeeze simultaneously some wider families of quantum states,…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
The IP matrix model is a simple large $N$ quantum mechanical model made up of an adjoint harmonic oscillator plus a fundamental harmonic oscillator. It is a model introduced previously as a toy model of the gauge theory dual of an AdS black…
Krylov quantum diagonalization methods have emerged as a promising use case for quantum computers. However, many existing implementations rely on controlled operations, which pose challenges to near-term quantum hardware. We introduce a…
Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains,…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
Commonly, the notion of "quantum chaos'' refers to the fast scrambling of information throughout complex quantum systems undergoing unitary evolution. Motivated by the Krylov complexity and the operator growth hypothesis, we demonstrate…
For any state in a $D$-dimensional Hilbert space with a choice of basis, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents the state on a discrete phase space. The Wigner function…
We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time…
The Bishop-Gromov bound -- a cousin of the focusing lemmas that Hawking and Penrose used to prove their black hole singularity theorems -- is a differential geometry result that upperbounds the rate of growth of volume of geodesic balls in…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
Pipelined Krylov methods seek to ameliorate the latency due to inner products necessary for projection by overlapping it with the computation associated with sparse matrix-vector multiplication. We clarify a folk theorem that this can only…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
Simultaneous treatment of neutrino oscillations and collisions in astrophysical environments requires the use of (quantum) kinetic equations. Despite major advances in the field of quantum kinetics, the structure of the kinetic equations…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
In the paper we consider the problem of the rigorous description of the kinetic evolution in the presence of initial correlations of quantum large particle systems. One of the developed approaches consists in the description of the…