Related papers: Using matrix-product states for time-series machin…
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,…
Identifying variational wave functions that efficiently parametrize the physically relevant states in the exponentially large Hilbert space is one of the key tasks towards solving the quantum many-body problem. Powerful tools in this…
Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…
This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\"odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating…
In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pad\'e and Arnoldi approximations to the evolution operator. By…
Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs…
Static disorder plays a crucial role in the electronic dynamics and spectroscopy of complex molecular systems. Traditionally, obtaining observables averaged over static disorder requires thousands of realizations via direct sampling of the…
Molecular Dynamics (MD) simulation is widely used to analyze the properties of molecules and materials. Most practical applications, such as comparison with experimental measurements, designing drug molecules, or optimizing materials, rely…
Time series data, including univariate and multivariate ones, are characterized by unique composition and complex multi-scale temporal variations. They often require special consideration of decomposition and multi-scale modeling to…
State-space models (SSMs) have recently attention as an efficient alternative to computationally expensive attention-based models for sequence modeling. They rely on linear recurrences to integrate information over time, enabling fast…
Multiple instance learning is an ideal mode of analysis for histopathology data, where vast whole slide images are typically annotated with a single global label. In such cases, a whole slide image is modelled as a collection of tissue…
In this paper, we propose a novel method of model-based time series clustering with mixtures of general state space models (MSSMs). Each component of MSSMs is associated with each cluster. An advantage of the proposed method is that it…
Quantification of system-wide perturbations from time series -omic data (i.e. a large number of variables with multiple measures in time) provides the basis for many downstream hypothesis generating tools. Here we propose a method,…
Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression…
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…
As in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is…
Ultra-short pulses propagating in nonlinear nanophotonic waveguides can simultaneously leverage both temporal and spatial field confinement, promising a route towards single-photon nonlinearities in an all-photonic platform. In this…
A matrix product state formulation of the multiconfiguration time-dependent Hartree (MPS-MCTDH) theory is presented. The Hilbert space that is spanned by the direct products of the phonon degree of freedoms, which is linearly parameterized…
We obtain an exact matrix-product-state (MPS) representation of a large series of fractional quantum Hall (FQH) states in various geometries of genus 0. The states in question include all paired k=2 Jack polynomials, such as the Moore-Read…
We introduce a method based on matrix product states (MPS) for computing spectral functions of (quasi) one-dimensional spin chains, working directly in momentum space in the thermodynamic limit. We simulate the time evolution after applying…