Related papers: Generating Function for Tensor Network Diagrammati…
Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of…
Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a…
Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical…
The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and…
Text summarization aims to compress a textual document to a short summary while keeping salient information. Extractive approaches are widely used in text summarization because of their fluency and efficiency. However, most of existing…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
Tensor networks have been an important concept and technique in many research areas, such as quantum computation and machine learning. We study the exponential complexity of contracting tensor networks on two special graph structures:…
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
As large-scale graphs become more widespread, more and more computational challenges with extracting, processing, and interpreting large graph data are being exposed. It is therefore natural to search for ways to summarize these expansive…
We define several new types of quantum chromatic numbers of a graph and characterise them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the…
Topology diagrams are widely seen in power system applications, but their automatic generation is often easier said than done. When facing power transmission systems with strongly-meshed structures, existing approaches can hardly produce…
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.…
Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…
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…
It is challenging to reduce the complexity of neural networks while maintaining their generalization ability and robustness, especially for practical applications. Conventional solutions for this problem incorporate quantum-inspired neural…
Tensor network states and parton wave functions are two pivotal methods for studying quantum many-body systems. This work connects these two subjects as we demonstrate that a variety of parton wave functions, such as projected Fermi sea and…
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 quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…