Related papers: Continuous matrix product states for non-relativis…
In these lectures notes, we review our recent works addressing various problems of finding the nearest stable system to an unstable one. After the introduction, we provide some preliminary background, namely, defining Port-Hamiltonian…
We present an algorithm for studying quantum systems at finite temperature using continuous matrix product operator representation. The approach handles both short-range and long-range interactions in the thermodynamic limit without…
Many one-dimensional lattice particle models with open boundaries, like the paradigmatic Asymmetric Simple Exclusion Process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not…
Models whose ground states can be written as an exact matrix product state (MPS) provide valuable insights into phases of matter. While MPS-solvable models are typically studied as isolated points in a phase diagram, they can belong to a…
Towards the efficient simulation of near-term quantum devices using tensor network states, we introduce an improved real-space parallelizable matrix-product state (MPS) compression method. This method enables efficient compression of all…
A bang-bang (BB) algorithm prepares the ground state of a lattice quantum many-body Hamiltonian $H=H_1+H_2$ by evolving an initial product state alternating between $H_1$ and $H_2$. We optimize the algorithm with tensor networks in one and…
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 study the set of random matrix product states (RMPS) introduced in arXiv:0908.3877 as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical…
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…
This work presents a comparative study of new and existing optimization and diagonalization methods for solving time-independent partial differential equations (PDEs) using matrix product states (MPS) in the quantized tensor-train formalism…
We present a suite of "holographic" quantum algorithms for efficient ground-state preparation and dynamical evolution of correlated spin-systems, which require far-fewer qubits than the number of spins being simulated. The algorithms…
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…
To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansatzes. We perform variational energy minimization with respect to a…
Resolving unsteady transport phenomena in geometrically complex domains is traditionally constrained by polynomial scaling of computational cost with spatial resolution. While methods based on tensor-network data representations or…
We present a state-interaction approach for matrix product state (MPS) wave functions in a nonorthogonal molecular orbital basis. Our approach allows us to calculate for example transition and spin-orbit coupling matrix elements between…
In the era of noisy, intermediate-scale quantum (NISQ) devices, the efficient preparation of many-body resource states is a task of paramount importance. In this paper we focus on the deterministic preparation of matrix-product states (MPS)…
Correlator product states (CPS) are a class of tensor network wavefunctions applicable to strongly correlated problems in arbitrary dimensions. Here, we present a method for optimizing and evaluating the energy of the CPS wavefunction that…
We prove that every injective Matrix Product State is the unique ground state of a simple hopping theory. We start by studying the low energy spectrum of parent Hamiltonians of injective Matrix Product States in a particular long range and…
The uncertainties in material and other properties of structures are usually spatially correlated. We introduce an efficient technique for representing and processing spatially correlated random fields in robust topology optimisation of…
An extension of the projected entangled-pair states (PEPS) algorithm to infinite systems, known as the iPEPS algorithm, was recently proposed to compute the ground state of quantum systems on an infinite two-dimensional lattice. Here we…