Related papers: Numerically efficient unitary evolution for Hamilt…
We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of…
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…
In this work, we combine an established method for open quantum systems -- the time evolving density matrix using orthogonal polynomials algorithm (TEDOPA) -- with the transfer tensors formalism (TTM), a new tool for the analysis,…
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…
A large, or even infinite, local Hilbert space dimension poses a significant computational challenge for simulating quantum systems. In this work, we present a matrix product state (MPS)-based method for simulating one-dimensional quantum…
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…
The numerically exact path integral Monte Carlo approach for the real-time evolution of dissipative quantum systems (PIMC), particularly suited for systems with discrete configuration space (tight-binding systems), is extended to treat…
Quantum trajectories and superoperator algorithms implemented within the matrix product state (MPS) framework are powerful tools to simulate the real-time dynamics of open dissipative quantum systems. As for the unitary case, the reachable…
The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with…
We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an…
We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate…
Accurately simulating the non-Markovian dynamics of open quantum systems remains a significant challenge. While the recently proposed time-evolving matrix product operator (TEMPO) algorithm based on path integrals successfully circumvents…
We review different tensor network approaches to study the spreading of operators in generic nonintegrable quantum systems. As a common ground to all methods, we quantify this spreading by means of the Frobenius norm of the commutator of a…
Matrix product states (MPS) are a central language for one-dimensional quantum matter and a practical target for near-term quantum simulators and variational algorithms. Yet, while substantial effort has focused on preparing MPS with…
Simulating many-body open quantum systems is an extremely challenging problem, with methods often restricted to either models with nearest-neighbor interactions or semi-classical approximations. In particular, modeling two-dimensional…
We propose a tensor-network (TN) approach for solving classical optimization problems that is inspired by spectral filtering and sampling on quantum states. We first shift and scale an Ising Hamiltonian of the cost function so that all…
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…
The inverse problem of 'eigenstates-to-Hamiltonian' is considered for an open chain of $N$ quantum spins in the context of Many-Body-Localization. We first construct the simplest basis of the Hilbert space made of $2^N$ orthonormal…
The process tensor framework to open quantum systems provides the most general description of multi-time correlations in non-Markovian quantum dynamics. A compressed representation of a process tensor in terms of matrix product operators…
In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings, or to…