Related papers: Efficient Matrix Product State Method for periodic…
We derive an exact canonical matrix product state (MPS) representation for Dicke states $|D^n_k\rangle$ with minimal bond dimension $\chi=k+1$, for general values of $n$ and $k$, for which the W-state is the simplest case $k=1$. We use this…
We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…
We derive an exact formula for a matrix product state (MPS) representation (or a PEPS in higher number of dimensions) of the ground state of translationally invariant bosonic lattice systems in terms of a single one-dimensional Euclidean…
We introduce Gaussian Matrix Product States (GMPS), a generalization of Matrix Product States (MPS) to lattices of harmonic oscillators. Our definition resembles the interpretation of MPS in terms of projected maximally entangled pairs,…
We discuss the relations between restricted Boltzmann machine (RBM) states and the matrix product states (MPS) for the ground states of 1D translational invariant stabilizer codes. A generic translational invariant and finitely connected…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…
We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed…
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…
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…
Matrix product states (MPS) are a standard tensor-network representation for ground states of one-dimensional quantum many-body systems, and they underpin widely used simulation tools such as DMRG. However, while quantum model checking has…
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…
Density matrix renormalization group (DMRG) or matrix product states (MPS) is the most effective and accurate method for studying one-dimensional quantum many-body systems. However, the application of DMRG to two-dimensional systems is not…
We define matrix product states in the continuum limit, without any reference to an underlying lattice parameter. This allows to extend the density matrix renormalization group and variational matrix product state formalism to quantum field…
This work is devoted to the study Translation-Invariant (TI) Matrix Product State (MPS) representations of quantum states with periodic boundary conditions (PBC). We pursue two directions: we introduce new methods for constructing TI MPS…
Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence Matrix Product State (MPS) methods based on moderate entanglement have…
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…
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…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…