Related papers: Efficient description of many-body systems with Ma…
The advent of quantum computers promises exponential speed ups in the execution of various computational tasks. While their capabilities are hindered by quantum decoherence, they can be exactly simulated on classical hardware at the cost of…
In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements. Our method is exponentially faster than standard tomography, and it can also be used to certify that…
We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix…
We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $\chi$. Specifically, we consider ensembles produced by: (i) random sequential…
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…
Charge and energy transfer in biological and synthetic organic materials are strongly influenced by the coupling of electronic states to high-frequency underdamped vibrations under dephasing noise. Non-perturbative simulations of these…
Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In…
We develop the continuous matrix-product states approach for description of inhomogeneous one-dimensional quantum systems with long-range interactions. The method is applied to the exactly-solvable Calogero-Moser model. We show the high…
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 two results which combined enable one to reliably detect multimode, multipartite entanglement in the presence of measurement errors. The first result leads to a method to compute the best (approximated) physical covariance matrix…
A key feature of ground states of gapped local 1D Hamiltonians is their relatively low entanglement --- they are well approximated by matrix product states (MPS) with bond dimension scaling polynomially in the length $N$ of the chain, while…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by…
We show that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a 1D tensor network (matrix-product state) despite the presence…
The entanglement quantification and classification of multipartite quantum states are two important research fields in quantum information. In this work, we study the entanglement of arbitrary-dimensional multipartite pure states by looking…
Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also…
Area laws for entanglement in quantum many-body systems give useful information about their low-temperature behaviour and are tightly connected to the possibility of good numerical simulations. An intuition from quantum many-body physics…
Large-scale Markov decision processes (MDPs) require planning algorithms with runtime independent of the number of states of the MDP. We consider the planning problem in MDPs using linear value function approximation with only weak…