Related papers: On Krylov complexity in open systems: an approach …
We develop an extension of the Monte Carlo wave function approach that unambiguously identifies dynamical entanglement in general composite, open systems. Our algorithm performs tangential projections onto the set of separable states,…
We investigate how a thermodynamical first-order phase transition affects the dynamical chaotic behaviour of a given model. To this effect, we analyze the model of Berkooz, Brukner, Jia and Mamroud that interpolates between the…
Krylov complexity, a quantum complexity measure which uniquely characterizes the spread of a quantum state or an operator, has recently been studied in the context of quantum chaos. However, the definitiveness of this measure as a chaos…
Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often…
This paper is devoted to the study of behavior of open quantum systems consistently based on the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation which covers evolution in situations when decoherence can be distinguished. We…
Shifted Laplacian multigrid preconditioner has become a tool du jour for solving highly indefinite Helmholtz equations. The idea is to add a complex damping to the original Helmholtz operator and then apply a multigrid processing to the…
Flexible Krylov methods are a common standpoint for inverse problems. In particular, they are used to address the challenges associated with explicit variational regularization when it goes beyond the two-norm, for example involving an…
We investigate Krylov spread complexity for the ground state of two-band Hamiltonians, where the reference state is a generic state on the Bloch sphere. The spread complexity is obtained by using a purely geometric formulation in terms of…
In this work we introduce a memory-efficient method for computing the action of a Hermitian matrix function on a vector. Our method consists of a rational Lanczos algorithm combined with a basis compression procedure based on rational…
Many scientific applications require the solution of large initial-value problems, such as those produced by the method of lines after semi-discretization in space of partial differential equations. The computational cost of implicit time…
We develop a recursive perturbative expansion for the time-convolutionless (TCL) generator of an open quantum system in a generalized Lindblad form. This formulation provides a systematic approach to derive the generator at arbitrary order…
Competition between short- and long-range interactions underpins many emergent phenomena in nature. Despite rapid progress in their experimental control, computational methods capable of accurately simulating open quantum many-body systems…
We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector…
We study operator spreading in many-body quantum systems by its potential to generate an informationally complete measurement record in quantum tomography. We adopt continuous weak measurement tomography for this purpose. We generate the…
Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner-outer GMRES…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
We consider the linear least squares problem with linear equality constraints (LSE problem) formulated as $\min_{x\in\mathbb{R}^{n}}\|Ax-b\|_2 \ \mathrm{s.t.} \ Cx = d$. Although there are some classical methods available to solve this…
We consider finite-dimensional many-body quantum systems described by time-independent Hamiltonians and Markovian master equations, and present a systematic method for constructing smaller-dimensional, reduced models that exactly reproduce…
One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals. To date the only quantitative match is the equality between the Krylov spread complexity in triple-scaled SYK at…
In this paper, we propose a primal-dual splitting algorithm for a broad class of structured composite monotone inclusions that involve finitely many set-valued operators, compositions of set-valued operators with bounded linear operators,…