Related papers: Low-rank Tree Tensor Network Operators for Long-Ra…
We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of…
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…
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 new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast…
Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We…
High-fidelity electromagnetic (EM) simulations are indispensable for the design of microwave and wave devices, yet repeated full-wave evaluations over high-dimensional design spaces are often computationally prohibitive. While neural…
Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…
We discuss extended definitions of linear and multilinear operations such as Kronecker, Hadamard, and contracted products, and establish links between them for tensor calculus. Then we introduce effective low-rank tensor approximation…
Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely…
Feynman diagrams are an essential tool for simulating strongly correlated electron systems. However, stochastic quantum Monte Carlo sampling suffers from the sign problem, particularly when solving a multiorbital quantum impurity model.…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
The hierarchical equations of motion (HEOM) method is a numerically exact open quantum system dynamics approach. The method is rooted in an exponential expansion of the bath correlation function, which in essence strategically reshapes a…
We introduce T-Basis, a novel concept for a compact representation of a set of tensors, each of an arbitrary shape, which is often seen in Neural Networks. Each of the tensors in the set is modeled using Tensor Rings, though the concept…
The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…
In this paper, a hierarchical Tucker low-rank (HTLR) matrix is proposed to approximate non-oscillatory kernel functions in linear complexity. The HTLR matrix is based on the hierarchical matrix, with the low-rank blocks replaced by Tucker…
Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…
Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head-on. Therefore, developing reduced dimensionality representations that encapsulate…
This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…
Long Short Term Memory(LSTM) models are the building blocks of many state-of-the-art natural language processing(NLP) and speech enhancement(SE) algorithms. However, there are a large number of parameters in an LSTM model. This usually…
We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a…