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Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…

The advancement of diverse generative deep learning models and their variants has furnished substantial insights for investigating quantum many-body problems. In this work, we design two models based on the foundational architecture of…

Inspired by the advancements in large language models based on transformers, we introduce the transformer quantum state (TQS): a versatile machine learning model for quantum many-body problems. In sharp contrast to Hamiltonian/task specific…

By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such as SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make…

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…

Generalized symmetries have emerged as a powerful organizing principle for exotic quantum phases. However, their role in open quantum systems, especially for non-invertible cases, remains largely unexplored. We address this by applying a…

Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable…

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…

Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…

Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial…

Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the…

We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…

Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state,…

The task of classifying the entanglement properties of a multipartite quantum state poses a remarkable challenge due to the exponentially increasing number of ways in which quantum systems can share quantum correlations. Tackling such…

The interplay of quantum and classical simulation and the delicate divide between them is in the focus of massively parallelized tensor network state (TNS) algorithms designed for high performance computing (HPC). In this contribution, we…

We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…

Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes…

Matrix-product states (MPS) have proven to be a versatile ansatz for modeling quantum many-body physics. For many applications, and particularly in one-dimension, they capture relevant quantum correlations in many-body wavefunctions while…

Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…

Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…