Related papers: Improved local truncation schemes for the higher-o…
We explain an algorithm that approximately but efficiently assesses particular parity-check error-correcting codes of large, but finite, blocklength. This algorithm is based on the ``renormalization-group'' approach from physics: the idea…
It has proved difficult to extend the density matrix renormalization group technique to large two-dimensional systems. In this Communication I present a novel approach where the calculation is done directly in two dimensions. This makes it…
Loopy tensor networks have internal correlations that often make their compression inefficient. We show that even local bond optimization can make better use of the insight it has locally into relevant loop correlations. By cutting the…
We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor…
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…
Deep neural networks (DNN) can be applied at the post-processing stage for the improvement of the results of quantum computations on noisy intermediate-scale quantum (NISQ) processors. Here, we propose a method based on this idea, which is…
Designing superconducting quantum hardware requires simulation tools that can account for various deviations from ideal scenarios. This, in turn, requires approaches that automatically detect certain structures and leverage them to make the…
This paper studies the computational and statistical aspects of quantile and pseudo-Huber tensor decomposition. The integrated investigation of computational and statistical issues of robust tensor decomposition poses challenges due to the…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation…
The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…
We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization (TEFR) approach that…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
In this paper, we focus on the fixed TT-rank and precision problems of finding an approximation of the tensor train (TT) decomposition of a tensor. Note that the TT-SVD and TT-cross are two well-known algorithms for these two problems.…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
Quasi-Newton (QN) methods provide an efficient alternative to second-order methods for minimizing smooth unconstrained problems. While QN methods generally compose a Hessian estimate based on one secant interpolation per iteration,…
We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
A cascadic tensor multigrid method and an economic cascadic tensor multigrid method is presented for solving the image restoration models. The methods use quadratic interpolation as prolongation operator to provide more accurate initial…
We introduce a new class of finite differences schemes to approximate one dimensional dissipative semilinear hyperbolic systems with a BGK structure. Using precise analytical time-decay estimates of the local truncation error, it is…