Related papers: An Optimally Accurate Lanczos Algorithm in the Mat…
In this work, we develop a stochastic matrix product state (stoMPS) approach that combines the MPS technique and Monte Carlo samplings and can be applied to simulate quantum lattice models down to low temperature. In particular, we exploit…
We analyze the Lanczos method for matrix function approximation (Lanczos-FA), an iterative algorithm for computing $f(\mathbf{A}) \mathbf{b}$ when $\mathbf{A}$ is a Hermitian matrix and $\mathbf{b}$ is a given vector. Assuming that $f :…
Low rank tensor representation (LRTR) methods are very useful for hyperspectral anomaly detection (HAD). To overcome the limitations that they often overlook spectral anomaly and rely on large-scale matrix singular value decomposition, we…
We study the Lanczos algorithm where the initial vector is sampled uniformly from $\mathbb{S}^{n-1}$. Let $A$ be an $n \times n$ Hermitian matrix. We show that when run for few iterations, the output of Lanczos on $A$ is almost…
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
We show that the standard Lanczos algorithm can be efficiently implemented statistically and self consistently improved, using the stochastic reconfigurat ion method, which has been recently introduced to stabilize the Monte Carlo sign…
This is an introductory course to the Lanczos Method and Density Matrix Renormalization Group Algorithms(DMRG), two among the leading numerical techniques applied in studies of low-dimensional quantum models. The idea of studying the models…
Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are…
Matrix product operators (MPOs) provide a scalable approach for quantum state tomography (QST) by offering a compact representation of many-body mixed states with limited entanglement, using only a number of parameters that scales…
In this paper we propose and analyze an algorithm for identifying spectral gaps of a real symmetric matrix $A$ by simultaneously approximating the traces of spectral projectors associated with multiple different spectral slices. Our method…
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…
Variance reduction is a crucial idea for Monte Carlo simulation and the stochastic Lanczos quadrature method is a dedicated method to approximate the trace of a matrix function. Inspired by their advantages, we combine these two techniques…
In the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases…
We demonstrate that the optimal states in lossy quantum interferometry may be efficiently simulated using low rank matrix product states. We argue that this should be expected in all realistic quantum metrological protocols with…
Explicitly correlated methods, such as the transcorrelated method which shifts a Jastrow or Gutzwiller correlator from the wave function to the Hamiltonian, are designed for high-accuracy calculations of electronic structures, but their…
Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT) / matrix product states (MPS) representation. Both methods empower the traditional alternating…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
The least absolute shrinkage and selection operator (Lasso) is widely recognized across various fields of mathematics and engineering. Its variant, the generalized Lasso, finds extensive application in the fields of statistics, machine…
We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and…
The method of quantum Lanczos recursion is extended to solve for multiple excitations on the quantum computer. While quantum Lanczos recursion is in principle capable of obtaining excitations, the extension to a block Lanczos routine can…