Related papers: Loop-Free Tensor Networks for High-Energy Physics
In this technical paper we introduce the Tensor Network Theory (TNT) library -- an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The…
TENSO is a versatile and powerful open-source software package for numerically exact simulations of the dynamics of quantum systems immersed in structured thermal environments. It is based on a tree tensor network decomposition of the…
Computing free energy is a fundamental problem in statistical physics. Recently, two distinct methods have been developed and have demonstrated remarkable success: the tensor-network-based contraction method and the neural-network-based…
Accurate free energy representations are crucial for understanding phase dynamics in materials. We employ a scale-bridging approach to incorporate atomistic information into our free energy model by training a neural network on DFT-informed…
Tensor network methods provide an intuitive graphical language to describe quantum states, channels, open quantum systems and a class of numerical approximation methods that efficiently simulate certain many-body states in one spatial…
We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be…
We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…
The field of high-energy physics (HEP), along with many scientific disciplines, is currently experiencing a dramatic influx of new methodologies powered by modern machine learning techniques. Over the last few years, a growing body of HEP…
The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…
Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…
Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems,…
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…
When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the…
We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
We propose a novel neural network embedding approach to model power transmission grids, in which high voltage lines are disconnected and reconnected with one-another from time to time, either accidentally or willfully. We call our…
We describe an approach to fix the gauge degrees of freedom in tensor networks, including those with closed loops, which allows a canonical form for arbitrary tensor networks to be realized. Additionally, a measure for the internal…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…