Related papers: Loop-Free Tensor Networks for High-Energy Physics

A new renormalization group approach that maps lattice problems to tensor networks may hold the key to solving seemingly intractable models of strongly correlated systems in any dimension. A Physics Viewpoint on arXiv:0903.1069

A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and…

This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to…

Situated as a language between computer science, quantum physics and mathematics, tensor network theory has steadily grown in popularity and can now be found in applications ranging across the entire field of quantum information processing.…

We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…

Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…

We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert…

It is a critical challenge to simultaneously gain high interpretability and efficiency with the current schemes of deep machine learning (ML). Tensor network (TN), which is a well-established mathematical tool originating from quantum…

We analyze the tensor network loop cluster expansion, introduced in [G. Park, J. Gray, and G. K.-L. Chan, Phys. Rev. B 112, 174310 (2025)] as a systematic correction to belief propagation, in the context of general quantum many-body…

The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better…

We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…

Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it…

Tensor network formalisms have emerged as powerful tools for simulating quantum state evolution. While widely applied in the study of optical quantum circuits, such as Boson Sampling, existing tensor network approaches fail to address the…

Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum…

Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which…

We present a systematic study of Tensor Network (TN) models $\unicode{x2013}$ Matrix Product States (MPS) and Tree Tensor Networks (TTN) $\unicode{x2013}$ for real-time jet tagging in high-energy physics, with a focus on low-latency…