Related papers: Environment-matrix-product operator for boundary-f…
We present a new method for compressing matrix product operators (MPOs) which represent sums of local terms, such as Hamiltonians. Just as with area law states, such local operators may be fully specified with a small amount of information…
We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space…
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…
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…
Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs…
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 form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the "area law". In…
Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the…
Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of…
The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…
Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited in…
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…
We provide theory, algorithms, and simulations of non-equilibrium quantum systems using a one-dimensional (1D) completely-positive (CP), matrix-product (MP) density-operator ($\rho$) representation. By generalizing the matrix product…
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…
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial…
Matrix product states (MPSs) and matrix product operators (MPOs) are fundamental tools in the study of quantum many-body systems, particularly in the context of tensor network methods such as Time-Evolving Block Decimation (TEBD). However,…
Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise…
We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications in a…
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 propose a way to construct a thermal pure quantum matrix product state (TPQ-MPS) that can simulate finite temperature quantum many-body systems with a minimal numerical cost comparable to the matrix product algorithm for the ground…