Related papers: Neural Network Matrix Product Operator: A Multi-Di…

We provide an exact construction of interaction Hamiltonians on a one-dimensional lattice which grow as a polynomial multiplied by an exponential with the lattice site separation as a matrix product operator (MPO), a type of one-dimensional…

Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide…

We provide a description of virtual non-local matrix product operator (MPO) symmetries in projected entangled pair state (PEPS) representations of string-net models. Given such a PEPS representation, we show that the consistency conditions…

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such…

Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural…

Here we assess two machine-learned potentials, one using the symmetric gradient domain machine learning (sGDML) method and one based on permutationally invariant polynomials (PIPs). These are successors to a PIP potential energy surface…

Numerical methods for obtaining exact dynamics of non-Markovian open quantum systems are mostly limited to either small systems or to short-time evolution only. Here, we propose a new algorithm for computing process tensors--matrix product…

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…

Neural network potentials (NNPs) enable large-scale molecular dynamics (MD) simulations of systems containing >10,000 atoms with the accuracy comparable to ab initio methods and play a crucial role in material studies. Although NNPs are…

Matrix Product Operators (MPOs) are tensor networks representing operators acting on 1D systems. They model a wide variety of situations, including communication channels with memory effects, quantum cellular automata, mixed states in 1D…

We present a first principles-quality potential energy surface (PES) describing the inter-atomic forces for hydrogen atoms interacting with free-standing graphene. The PES is a high-dimensional neural network potential that has been…

Machine Learning techniques can be used to represent high-dimensional potential energy surfaces for reactive chemical systems. Two such methods are based on a reproducing kernel Hilbert space representation or on deep neural networks. They…

The Matrix Element Method (MEM) is a powerful method to extract information from measured events at collider experiments. Compared to multivariate techniques built on large sets of experimental data, the MEM does not rely on an…

Implicit neural representations are powerful for geometric modeling, but their practical use is often limited by the high computational cost of network evaluations. We observe that implicit representations require progressively lower…

The ever-increasing data demand craves advancements in high-speed and energy-efficient computing hardware. Analog optical neural network (ONN) processors have emerged as a promising solution, offering benefits in bandwidth and energy…

This paper presents a novel pre-trained language models (PLM) compression approach based on the matrix product operator (short as MPO) from quantum many-body physics. It can decompose an original matrix into central tensors (containing the…

We show how to learn structures of generic, non-Markovian, quantum stochastic processes using a tensor network based machine learning algorithm. We do this by representing the process as a matrix product operator (MPO) and train it with a…

Artificial neural network (ANN) potentials enable highly accurate atomistic simulations of complex materials at unprecedented scales. Despite their promise, training ANN potentials to represent intricate potential energy surfaces (PES) with…

Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the…