Related papers: Multiseed Krylov complexity
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
We show that the characteristic function of the probability distribution associated with the change of an observable in a two-point measurement protocol with a perturbation can be written as an auto-correlation function between an initial…
We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first construct a sequence of reduced representations: the operator…
Quantum Krylov subspace diagonalization is a prominent candidate for early fault tolerant quantum simulation of many-body and molecular systems, but so far the focus has been mainly on computing ground-state energies. We go beyond this by…
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
The spatial distribution of interacting chemical fields is investigated in the non-diffusive limit. The evolution of fluid parcels is described by independent dynamical systems driven by chaotic advection. The distribution can be filamental…
We propose a tridiagonalization approach for non-Hermitian random matrices and Hamiltonians using singular value decomposition (SVD). This technique leverages the real and non-negative nature of singular values, bypassing the complex…
A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean-Vlasov limits of such system are formulated…
A novel theoretical convergence rate estimate for a Balancing Domain Decomposition by Constraints algorithm is proven for the solution of the cardiac Bidomain model, describing the propagation of the electric impulse in the cardiac tissue.…
Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time -- the most clear example being the Solar System -- but the situation for their quantum counterparts is less well understood. As a…
We examine the effective field theory (EFT) of maximal chaos through the lens of Krylov complexity and the Universal Operator Growth Hypothesis. We test the relationship between two measures of quantum chaos: out-of-time-ordered correlators…
The Lindblad description of an open quantum system gives rise to two types of integrability, since the nonequilibrium steady state can be integrable independently of the Liouvillian. Taking boundary-driven and dephasing spin chains as a…
We study operator complexity on various time scales with emphasis on those much larger than the scrambling period. We use, for systems with a large but finite number of degrees of freedom, the notion of K-complexity employed in…
Quantum annealing is a computational approach designed to leverage quantum fluctuations for solving large-scale classical optimization problems. Although incorporating standard transverse field (TF) terms in the annealing process can help…
We develop computational tools necessary to extend the application of Krylov complexity beyond the simple Hamiltonian systems considered thus far in the literature. As a first step toward this broader goal, we show how the Lanczos algorithm…
We investigate the delocalization of operators in non-chaotic quantum systems whose interactions are encoded in an underlying graph or network. In particular, we study how fast operators of different sizes delocalize as the network…
Quantum observables of generic many-body systems exhibit a universal pattern of growth in the Krylov space of operators. This pattern becomes particularly manifest in the Lanczos basis, where the evolution superoperator assumes the…