Related papers: Plaquette Renormalization Scheme for Tensor Networ…
We investigate the ground state of the spin $S=1/2$ Heisenberg anti-ferromagnet on the Shuriken lattice, also in the presence of an external magnetic field. To this end, we employ two-dimensional tensor network techniques based on infinite…
We propose a novel algorithm with a modified Tucker decomposition for tensor network that allows for efficiently and precisely calculating the ground state and thermodynamic properties of two-dimensional (2D) quantum spin lattice systems,…
The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the…
Low-rank recovery builds upon ideas from the theory of compressive sensing, which predicts that sparse signals can be accurately reconstructed from incomplete measurements. Iterative thresholding-type algorithms-particularly the normalized…
The renormalization group flows of the one-dimensional anisotropic XY model and quantum Ising model under a transverse field are obtained by different multiscale entanglement renormalization ansatz schemes. It is shown that the optimized…
On the lattice, a renormalization group (RG) flow for two-dimensional partition functions expressed as a tensor network can be obtained using the tensor network renormalization (TNR) algorithm [G. Evenbly, G. Vidal, Phys. Rev. Lett. 115…
This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for…
We present a new algorithm for transposing sparse tensors called Quesadilla. The algorithm converts the sparse tensor data structure to a list of coordinates and sorts it with a fast multi-pass radix algorithm that exploits knowledge of the…
Tensor network contraction is a fundamental mathematical operation that generalizes the dot product and matrix multiplication. It finds applications in numerous domains, such as database systems, graph theory, machine learning, probability…
The two-dimensional ferromagnetic anisotropic Ashkin-Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recover all the known exacts results for the…
We propose a tensor-network-based algorithm to study the classical Ising model on an infinitely large hyperbolic lattice with a regular 3D tesselation of identical dodecahedra. We reformulate the corner transfer matrix renormalization group…
Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…
Finite expressions for the mean value of the stress tensor corresponding to a scalar field with a generalized dispersion relation in a Friedman--Robertson--Walker universe are obtained using adiabatic renormalization. Formally divergent…
Our aim is to compute the lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon on the lattice. The theoretical basis of the calculation is the operator product expansion. To construct operators…
We study the ground-state properties of the two-dimensional quantum spin systems having the valence-bond-solid (VBS) type ground states. The ``product-of-tensors'' form of the ground-state wavefunction of the system is utilized to associate…
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the…
We systematically map low-bond-dimension PEPs tensor networks to quantum circuits. By measuring and reusing qubits, we demonstrate that a simulation of an $N \times M$ square-lattice PEPs network, for arbitrary $M$, of bond dimension $2$…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…
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…