Related papers: Efficient Tensor Network ansatz for high-dimension…
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent…
We propose a qubit efficient scheme to study ground state properties of quantum many-body systems on near-term noisy intermediate scale quantum computers. One can obtain a tensor network representation of the ground state using a number of…
We apply a series of projection techniques on top of tensor networks to compute energies of ground state wave functions with higher accuracy than tensor networks alone with minimal additional cost. We consider both matrix product states as…
Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop…
Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which…
Recently developed tensor network methods demonstrate great potential for addressing the quantum many-body problem, by constructing variational spaces with polynomially, instead of exponentially, scaled parameters. Constructing such an…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…
A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, how to extract the…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
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…
Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
We introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler…
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…
We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle…
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…
Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…
The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global…
We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of one-dimensional matrix-product states to tensor…