Related papers: Effective One-Dimensional Models from Matrix Produ…
In one-dimensional quantum systems with short-range interactions, a set of leading numerical methods is based on matrix product states, whose bond dimension determines the amount of computational resources required by these methods. We…
We present a method of extracting information about topological order from the ground state of a strongly correlated two-dimensional system represented by an infinite projected entangled pair state (iPEPS). As in Phys. Rev. B 101, 041108…
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…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
Quantum many body physics simulations with Matrix Product States can often be accelerated if the quantum symmetries present in the system are explicitly taken into account. Conventionally, quantum symmetries have to be determined before…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
We present a matrix-product-state-based numerical approach for simulating systems composed of several qubits and a common one-dimensional waveguide. In the presented approach, the one-dimensional waveguide is modeled in real space. Thus,…
We develop a new projected wave function approach which is based on projection operators in the form of matrix-product operators (MPOs). Our approach allows to variationally improve the short range entanglement of a given trial wave…
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…
Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…
We construct matrix product steady state for a class of interacting particle systems where particles do not obey hardcore exclusion, meaning each site can occupy any number of particles subjected to the global conservation of total number…
Stationary states of stochastic models, which have $N$ states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite $M$-dimensional matrix product state for any ${N,M}$. Second,…
Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely…
It is known that exact traveling wave solutions exist for families of (n+1)-states stochastic one-dimensional non-equilibrium lattice models with open boundaries provided that some constraints on the reaction rates are fulfilled. These…
We propose a general method for deriving one-dimensional models for nonlinear structures. It captures the contribution to the strain energy arising not only from the macroscopic elastic strain as in classical structural models, but also…
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…
We investigate the application of matrix product states to the Hubbard model in one spatial dimension with both of open and periodic boundary conditions. We develop the variatinal method that the optimization of the variational parameters…
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…
Generative models hold the promise of significantly expediting the materials design process when compared to traditional human-guided or rule-based methodologies. However, effectively generating high-quality periodic structures of materials…
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…