Related papers: Adaptive variational low-rank dynamics for open qu…
I describe a simple algorithm for numerically finding the ground state and low-lying excited states of a quantum system. The algorithm is an adaptation of the relaxation method for solving Poisson's equation, and is fundamentally based on…
We present a novel method to approximate optimal feedback laws for nonlinear optimal control based on low-rank tensor train (TT) decompositions. The approach is based on the Dirac-Frenkel variational principle with the modification that the…
An adaptive method for parabolic partial differential equations that combines sparse wavelet expansions in time with adaptive low-rank approximations in the spatial variables is constructed and analyzed. The method is shown to converge and…
The structure of the initial system-environment state is fundamental to determining the nature and characteristics of the evolution of such an open quantum system. The usual assumption is to consider that the initial system-environment…
The dynamics of open quantum systems is governed by the Lindblad master equation, which provides a consistent framework for incorporating environmental effects into the evolution of the system. Since exact solutions are rarely available,…
We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators, which ensure the density matrix retains its Gaussian form…
A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics that can be described by the Lindblad master equation in Liouville density operator space. The method extends the Hilbert space…
Extensive efforts have been made to boost the performance in the domain of language models by introducing various attention-based transformers. However, the inclusion of linear layers with large dimensions contributes to significant…
In this paper, we develop a framework for designing arbitrary high order low-rank schemes for the Lindblad equation with time-dependent Hamiltonians. Our approach is based on nested Picard iterative integrators (NPI) and results in schemes…
This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…
Every open-system dynamics can be associated to infinitely many stochastic pictures, called unravelings, which have proved to be extremely useful in several contexts, both from the conceptual and the practical point of view. Here, focusing…
Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…
We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected Variational Quantum Dynamics (pVQD) algorithm, that performs a global optimization with linear…
We examine the effectiveness of Lindblad master equation in capturing the short-time dynamics of entanglement and purity in open quantum systems. Focusing on two interacting two-level systems interacting with a larger environment, we…
The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally-local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the…
We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${\cal H}_0$ of the system, and targeting a unique dark state in ${\cal…
We present a collection of methods to simulate entangled dynamics of open quantum systems governed by the Lindblad equation with tensor network methods. Tensor network methods using matrix product states have been proven very useful to…
We provide model reduction formulas for open quantum systems consisting of a target component which weakly interacts with a strongly dissipative environment. The time-scale separation between the uncoupled dynamics and the interaction…
Master equations are a useful tool to describe the evolution of open quantum systems. In order to characterize the mathematical features and the physical origin of the dynamics, it is often useful to consider different kinds of master…
Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators. Yet rigorous methods for time-dependent Hamiltonians and Lindbladians remain scarce despite their wide use. We close this gap by learning the…