Related papers: Space Reduction in Matrix Product State
Reduced model spaces, such as reduced basis and polynomial chaos, are linear spaces $V_n$ of finite dimension $n$ which are designed for the efficient approximation of families parametrized PDEs in a Hilbert space $V$. The manifold…
Quantum computing is finding promising applications in optimization, machine learning and physics, leading to the development of various models for representing quantum information. Because these representations are often studied in…
A zero-site density matrix renormalization algorithm (DMRG0) is proposed to minimize the energy of matrix product states (MPS). Instead of the site tensors themselves, we propose to optimize sequentially the "message" tensors between…
Matrix product density operators (MPDOs) are tensor network representations of locally purified density matrices where each physical degree of freedom is associated to an environment degree of freedom. MPDOs have interesting properties for…
In this paper we give an introduction to the numerical density matrix renormalization group (DMRG) algorithm, from the perspective of the more general matrix product state (MPS) formulation. We cover in detail the differences between the…
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…
Incorporating conservation laws explicitly into matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used…
We show how to efficiently simulate pure quantum states in one dimensional systems that have both finite energy density and vanishingly small energy fluctuations. We do so by studying the performance of a tensor network algorithm that…
Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary…
Matrix product state (MPS) offers a framework for encoding classical data into quantum states, enabling the efficient utilization of quantum resources for data representation and processing. This research paper investigates techniques to…
Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and…
We demonstrate that the optimal states in lossy quantum interferometry may be efficiently simulated using low rank matrix product states. We argue that this should be expected in all realistic quantum metrological protocols with…
As in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is…
In the fields of quantum mechanics and quantum information science, the traces of reduced density matrix powers play a crucial role in the study of quantum systems and have numerous important applications. In this paper, we propose a…
This paper revisits the problem of decomposing a positive semidefinite matrix as a sum of a matrix with a given rank plus a sparse matrix. An immediate application can be found in portfolio optimization, when the matrix to be decomposed is…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…
Ground-state preparation is a fundamental task in quantum simulation, because the overlap of the prepared state with the true ground state significantly affects the overall cost of subsequent quantum algorithms. We propose a three-stage…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
This is the first of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The non-zero entries in the output are chosen to…