相关论文: Local Matrix Product Operators: Canonical Form, Co…

We present some exact results for the optimal Matrix Product State (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce…

Local-operator entanglement (LOE) quantifies the nonlocal structure of Heisenberg operators and serves as a diagnostic of many-body chaos. We provide rigorous bounds showing when an operator can be well-approximated by a matrix-product…

We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground…

We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term…

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…

Theoretical understanding of strongly correlated systems in one spatial dimension (1D) has been greatly advanced by the density-matrix renormalization group (DMRG) algorithm, which is a variational approach using a class of…

Process tensor matrix product operators (PT-MPOs) enable numerically exact simulations for an unprecedentedly broad range of open quantum systems. By representing environment influences in MPO form, they can be efficiently compressed using…

In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…

Here we present an efficient and numerically stable procedure for compressing a correlation matrix into a set of local unitary single-particle gates, which leads to a very efficient way of forming the matrix product state (MPS)…

Matrix product operators (MPOs) provide a scalable approach for quantum state tomography (QST) by offering a compact representation of many-body mixed states with limited entanglement, using only a number of parameters that scales…

We present matrix-product state (MPS) based band Lanczos method as solver for quantum cluster methods such as the variational cluster approximation. While a na\"ive implementation of MPS as cluster solver would barely improve its range of…

Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state…

Numerical methods for obtaining exact dynamics of non-Markovian open quantum systems are mostly limited to either small systems or to short-time evolution only. Here, we propose a new algorithm for computing process tensors--matrix product…

Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various…

In this work, we develop a stochastic matrix product state (stoMPS) approach that combines the MPS technique and Monte Carlo samplings and can be applied to simulate quantum lattice models down to low temperature. In particular, we exploit…

The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…

Bosonic Gaussian states are ubiquitous in quantum optics and condensed matter physics. While they are efficiently handled within the Gaussian formalism, sampling requires calculating amplitudes in the boson occupation basis. This step,…

Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode…

Learning the closest matrix product state (MPS) representation of a quantum state enables useful tools for quantum machine learning and analysis of complex quantum systems. In this work, we study the problem of learning MPS in the following…

Matrix Product State (MPS) wavefunctions have many applications in quantum information and condensed matter physics. One application is to represent states in the thermodynamic limit directly, using a small set of position independent…