相关论文: Matrix product states approaches to operator sprea…

We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for…

We propose a tensor network framework for approximating the evolution of observables of measure-preserving ergodic systems. Our approach is based on a spectrally-convergent approximation of the skew-adjoint Koopman generator by a…

The Tucker decomposition generalizes the notion of Singular Value Decomposition (SVD) to tensors, the higher dimensional analogues of matrices. We study the problem of constructing the Tucker decomposition of sparse tensors on distributed…

Classical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial state. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation…

In the study of quantum chaos, `out of time ordered correlators' (OTOCs) are commonly used to quantify the rate at which quantum information is scrambled. This rate has been conjectured by Maldecena et al. to obey a universal, temperature…

Information scrambling and the butterfly effect in chaotic quantum systems can be diagnosed by out-of-time-ordered (OTO) commutators through an exponential growth and large late time value. We show that the latter feature shows up in a…

We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order…

Low-rank approximation using time-dependent bases (TDBs) has proven effective for reduced-order modeling of stochastic partial differential equations (SPDEs). In these techniques, the random field is decomposed to a set of deterministic…

Fast scrambling of quantum correlations, reflected by the exponential growth of Out-of-Time-Order Correlators (OTOCs) on short pre-Ehrenfest time scales, is commonly considered as a major quantum signature of unstable dynamics in quantum…

Recent theoretical and experimental studies have shown significance of quantum information scrambling (i.e. a spread of quantum information over a system degrees of freedom) for problems encountered in high-energy physics, quantum…

In this paper we will attempt to answer the following question: what are the natural quantum subsystems which emerge out of a system's dynamical laws? To answer this question we first define generalized tensor product structures (gTPS) in…

Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…

Local excitations as carriers of quantum information spread out in the system in ways governed by the underlying interaction and symmetry. Understanding this phenomenon, also called quantum scrambling, is a prerequisite for employing…

This document explores the connections between singular value decomposition (SVD) and various tensor operations in the context of quantum state calculations and tensor networks. The relationships between SVD and quantities such as trace,…

Gradient-based temporal difference (GTD) algorithms are widely used in off-policy learning scenarios. Among them, the two time-scale TD with gradient correction (TDC) algorithm has been shown to have superior performance. In contrast to…

We generalize the Time-Dependent Variational Principle (TDVP) to dissipative systems using Monte Carlo methods, allowing the application of existing variational classes for pure states, such as Matrix Product States (MPS), to the simulation…

We study information scrambling, as diagnosed by the out-of-time order correlations (OTOCs), in a system of large spins collectively interacting via spatially inhomogeneous and incommensurate exchange couplings. The model is realisable in a…

We study out-of-time-ordered correlators (OTOC) in hard-core boson models with short-range and long-range hopping and compare the results to the OTOC in the Luttinger liquid model. For the density operator, a related `commutator function'…

In recent times out-of-time-order correlators (OTOC) have been established as a tool to understand butterfly effects, quantum information scrambling, and many-body localization. They can also be useful in determining different phases of…

In this paper, we propose different algorithms for the solution of a tensor linear discrete ill-posed problem arising in the application of the meshless method for solving PDEs in three-dimensional space using multiquadric radial basis…