Related papers: Loop-Free Tensor Networks for High-Energy Physics
We demonstrate the use of tensor networks for image classification with the TensorNetwork open source library. We explain in detail the encoding of image data into a matrix product state form, and describe how to contract the network in a…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
We introduce an efficient method TTN-HEOM for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme to the…
We present a tensor-network-based method for simulating a weakly-measured quantum circuit. In particular, we use a Markov chain to efficiently sample measurements and contract the tensor network, propagating their effect forward along the…
Latent class models are powerful statistical modeling tools widely used in psychological, behavioral, and social sciences. In the modern era of data science, researchers often have access to response data collected from large-scale surveys…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. It does so by fusing concepts from network science and model-based systems…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Neural networks (NNs) are inherently multidimensional classifiers that learn complex, non-linear relationships among input observables. While their flexibility enables unprecedented performance in high-energy physics (HEP) analyses, it also…
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…
Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
Computing spectral functions in large, non-periodic super-moir\'e systems remains an open problem due to the exceptionally large system size that must be considered. Here, we establish a tensor network methodology that allows computing…
Gauged gaussian Projected Entangled Pair States are particular tensor network constructions that describe lattice states of fermionic matter interacting with dynamical gauge fields. We show how one can efficiently compute, using Monte-Carlo…
We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks…
The phase structure of the two dimensional lattice CP(1) model in the presence of the $\theta$ term is analyzed by tensor network methods. The tensor renormalization group, which is a standard renormalization method of tensor networks, is…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…