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We speed up thermal simulations of quantum many-body systems in both one- (1D) and two-dimensional (2D) models in an exponential way by iteratively projecting the thermal density matrix $\hat\rho=e^{-\beta \hat{H}}$ onto itself. We refer to…

We describe a computationally-efficient heuristic algorithm based on a renormalization-group procedure which aims at solving the problem of finding minimal surface given its boundary (curve) in any hypercubic lattice of dimension $D>2$. We…

We propose and implement an algorithm to calculate the norm and reduced density matrices of the antisymmetrized geminal power (AGP) of any rank with polynomial cost. Our method scales quadratically per element of the reduced density…

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the…

The tensor-network renormalization group (TNRG) is an accurate numerical real-space renormalization group method for studying phase transitions in both quantum and classical systems. Continuous phase transitions, as an important class of…

To avoid the combinatorial computational cost of configuration interaction (CI), we have previously introduced the symmetric tensor decomposition CI (STD-CI) method, where we take advantage of the antisymmetric nature of the electronic wave…

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…

We propose and test a scheme for entanglement renormalization capable of addressing large two-dimensional quantum lattice systems. In a translationally invariant system, the cost of simulations grows only as the logarithm of the lattice…

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

The ever-growing size of neural networks poses serious challenges on resource-constrained devices, such as embedded sensors. Compression algorithms that reduce their size can mitigate these problems, provided that model performance stays…

We propose an entanglement-based algorithm of the tensor-network strong-disorder renormalization group (tSDRG) method for quantum spin systems with quenched randomness. In contrast to the previous tSDRG algorithm based on the energy…

Density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. In this work, we develop a perturbation theory of DMRG (PT-DMRG) to largely increase its accuracy in an extremely…

We propose a numerical variational method for three-dimensional (3D) classical lattice models. We construct the variational state as a product of local tensors, and improve it by use of the corner transfer matrix renormalization group…

We report a complete implementation of the coupled-cluster method with single, double, and triple excitations (CCSDT) where tensor decompositions are used to reduce its scaling and overall computational costs. For the decomposition of the…

Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a `Wilson chain'. It was shown recently that Wilson chains for different…

We present an alternative, memory-efficient, Schmidt decomposition-based description of the inherently bipartite restricted active space (RAS) scheme, which can be implemented effortlessly within the density matrix renormalization group…

The density matrix renormalization group method is generalized to one dimensional random systems. Using this method, the energy gap distribution of the spin-1/2 random antiferromagnetic Heisenberg chain is calculated. The results are…

Algebraic multigrid (AMG) is an $\mathcal{O}(n)$ solution process for many large sparse linear systems. A hierarchy of progressively coarser grids is constructed that utilize complementary relaxation and interpolation operators. High-energy…