Related papers: Isometric Tensor Network States in Two Dimensions
Simulating quantum many-body systems (QMBS) is one of the long-standing, highly non-trivial challenges in condensed matter physics and quantum information due to the exponentially growing size of the system's Hilbert space. To date, tensor…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
Tensor networks (TNs) have been gaining interest as multiway data analysis tools owing to their ability to tackle the curse of dimensionality and to represent tensors as smaller-scale interconnections of their intrinsic features. However,…
We present a 2D bosonization duality using the language of tensor networks. Specifically, we construct a tensor network operator (TNO) that implements an exact 2D bosonization duality. The primary benefit of the TNO is that it allows for…
Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely…
We propose an efficient algorithm for simulating quantum many-body systems in two spatial dimensions using projected entangled pair states. This is done by approximating the environment, arising in the context of updating tensors in the…
Hybrid tensor networks offer a promising route to enhance the expressivity of classical tensor network methods by incorporating quantum states prepared on a quantum computer. Existing approaches are limited by the variational optimization…
Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…
Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time…
We revisit the application of neural networks techniques to quantum state tomography. We confirm that the positivity constraint can be successfully implemented with trained networks that convert outputs from standard feed-forward neural…
We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…
We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…
Tensor network (TN) representation is a powerful technique for computer vision and machine learning. TN structure search (TN-SS) aims to search for a customized structure to achieve a compact representation, which is a challenging NP-hard…
The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing…
This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for…
Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor network (TN)…
Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…
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…
An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…