Related papers: Tensor network simulations for nonorientable surfa…
We propose a vertex representation of the tensor network (TN) for classical spin systems on hyperbolic lattices. The tensors form a network of regular $p$-sided polygons ($p>4$) with the coordination number four. The response to multi-state…
This paper presents a geometric analysis of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. Due to the highly complicated structure of the associated sensing…
In the previous paper [arXiv:2210.10435], the nonlinear perturbation theory of cosmological density field is generalized to include the tensor-valued bias of astronomical objects, such as spins and shapes of galaxies and any other tensors…
The phase structure of the two dimensional lattice CP(1) model in the presence of the $\theta$ term is analyzed by tensor network methods. The tensor renormalization group, which is a standard renormalization method of tensor networks, is…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of…
We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the p-spin…
Surface reconstruction from raw point clouds has been studied for decades in the computer graphics community, which is highly demanded by modeling and rendering applications nowadays. Classic solutions, such as Poisson surface…
We propose a hybrid quantum-classical eigensolver to address the computational challenges of simulating strongly correlated quantum many-body systems, where the exponential growth of the Hilbert space and extensive entanglement render…
Phase transitions in a modified Nishimori model, including the model considered by Kitatani, on a two-dimensional square lattice are investigated using a tensor-network-based sampling scheme. In this model, generating bond configurations is…
Novel machine learning computational tools open new perspectives for quantum information systems. Here we adopt the open-source programming library TensorFlow to design multi-level quantum gates including a computing reservoir represented…
The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
An $n$-cross field is a locally-defined orthogonal coordinate system invariant with respect to the cubic symmetry group. Cross fields are finding wide-spread use in mesh generation, computer graphics, and materials science among many…
Several Tensor Basis Neural Network (TBNN) frameworks aimed at enhancing turbulence RANS modeling have recently been proposed in the literature as data-driven constitutive models for systems with known invariance properties. However,…
Rooted in group field theory and matrix models, random tensor models are a recent background-invariant approach to quantum gravity in arbitrary dimensions. Colored tensor models (CTM) generate random triangulated orientable…
The probability tomography approach developed for the scalar resistivity method is here extended to the 2D tensorial apparent resistivity acquisition mode. The rotational invariant derived from the trace of the apparent resistivity tensor…
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…
The canonical tensor rank approximation problem (TAP) consists of approximating a real-valued tensor by one of low canonical rank, which is a challenging non-linear, non-convex, constrained optimization problem, where the constraint set…
Formulating non-Abelian gauge theories as a tensor network is known to be challenging due to the internal degrees of freedom that result in the degeneracy in the singular value spectrum. In two dimensions, it is straightforward to 'trace…