相关论文: An introduction to numerical methods in low-dimens…

Based on the original idea of the density matrix renormalization group (DMRG), i.e. to include the missing boundary conditions between adjacent blocks of the blocked quantum system, we present a rigorous and nonperturbative mathematical…

Gradient descent algorithms on Riemannian manifolds have been used recently for the optimization of quantum channels. In this contribution, we investigate the influence of various regularization terms added to the cost function of these…

Recently, artificial intelligence for science has made significant inroads into various fields of natural science research. In the field of quantum many-body computation, researchers have developed numerous ground state solvers based on…

At low energies, the microscopic characteristics and changes of physical systems as viewed at different distance scales are described by universal scale invariant properties investigated by the Renormalization Group (RG) apparatus, an…

This paper deals with three technical ingredients of geometry for quantum information. Firstly, we give an algorithm to obtain diagonal basis matrices for submodules of the Z_{d}-module Z_{d}^{n} and we describe the suitable computational…

We propose a density matrix renormalization group (DMRG) technique at finite temperatures. As is the case of the ground state DMRG, we use a single-target state that is calculated by making use of a regulated polynomial expansion. Both…

The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…

Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning…

The reduced density matrix (RDM) is crucial in quantum many-body systems for understanding physical properties, including all local physical quantity information. This study aims to minimize various error constraints that causes challenges…

We propose a new implementation of real-space renormalization group (RG) transformations for quantum states on a lattice. Key to this approach is the removal of short-ranged entanglement, similar to Vidal's entanglement renormalization…

The numerical analysis of strongly interacting nanostructures requires powerful techniques. Recently developed methods, such as the time-dependent density matrix renormalization group (tDMRG) approach or the embedded-cluster approximation…

Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum…

The recently proposed Clifford augmented density matrix renormalization group (CA-DMRG) method seamlessly integrates Clifford circuits with matrix product states, and takes advantage of the expression power from both. CA-DMRG has been shown…

An extension of the the density matrix renormalization group (DMRG) method is presented. Besides the two groups or classes of block states considered in White's formulation, the retained $m$ states and the neglected ones, we introduce an…

We present a numerical implementation of the density matrix renormalization group (DMRG) using the discrete variable representation (DVR) basis set. One main advantage of using the local DVR basis sets is that the computations of…

In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that…

We present the Copupled Cluster (CC) method and the Density matrix Renormalization Grooup (DMRG) method in a unified way, from the perspective of recent developments in tensor product approximation. We present an introduction into recently…

Latent Diffusion Models (LDMs) capture the dynamic evolution of latent variables over time, blending patterns and multimodality in a generative system. Despite the proficiency of LDM in various applications, such as text-to-image…

Low-rank approximations of original samples are playing more and more an important role in many recently proposed mathematical models from data science. A natural and initial requirement is that these representations inherit original…

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…