Related papers: On Subsample Size of Quantile-Based Randomized Kac…
Motivated by the randomized sketch to solve a variety of problems in scientific computation, we improve both the maximal weighted residual Kaczmarz method and the randomized block average Kaczmarz method using two new randomized sketch…
The supersymmetric method is a powerful method for the evaluation of quenched averages in disordered systems. Among others, this method has been applied to the theory of S-matrix fluctuations, the theory of universal conductance…
We propose a theory to explain the experimental observed deviation from the Kibble-Zurek mechanism (KZM) scaling in rapidly quenched critical phase transition dynamics. There is a critical quench rate $\tau_{Q}^{c1}$ above it the KZM…
In this paper, by regarding the two-subspace Kaczmarz method [20] as an alternated inertial randomized Kaczmarz algorithm we present a new convergence rate estimate which is shown to be better than that in [20] under a mild condition.…
We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
The Kaczmarz method for solving a linear system $Ax = b$ interprets such a system as a collection of equations $\left\langle a_i, x\right\rangle = b_i$, where $a_i$ is the $i-$th row of $A$, then picks such an equation and corrects $x_{k+1}…
The Kaczmarz method (KZ) and its variants, which are types of stochastic gradient descent (SGD) methods, have been extensively studied due to their simplicity and efficiency in solving linear equation systems. The iterative thresholding…
Quantum annealing (QA) with a transverse field often fails to sample degenerate ground states fairly, limiting applicability to problems requiring diverse optimal solutions. Although Quantum Monte Carlo (QMC) is widely used to simulate QA,…
In this paper, we consider a novel two-dimensional randomized Kaczmarz method and its improved version with simple random sampling, which chooses two active rows with probability proportional to the square of their cross-product-like…
The Kaczmarz method is an efficient iterative algorithm for large-scale linear systems. However, its linear convergence rate suffers from ill-conditioned problems and is highly sensitive to the smallest nonzero singular value. In this work,…
We consider the problem of computing an approximation to the integral $I=\int_{[0,1]^d}f(x) dx$. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of $O(n^{-1/2})$ from $n$ independent random function evaluations.…
Quantum detector tomography (QDT) is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we utilize regularization to improve the QDT accuracy whenever the probe states are…
The crossing of a continuous phase transition gives rise to the formation of topological defects described by the Kibble-Zurek mechanism (KZM) in the limit of slow quenches. The KZM predicts a universal power-law scaling of the defect…
Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work about linear and nonlinear QR models. Specifically, nonparametric estimation of the…
We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential $\mu$. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for…
The Kibble-Zurek mechanism (KZM) captures the essential physics of nonequilibrium quantum phase transitions with symmetry breaking. KZM predicts a universal scaling power law for the defect density which is fully determined by the system's…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…
Matrix factorization techniques compute low-rank product approximations of high dimensional data matrices and as a result, are often employed in recommender systems and collaborative filtering applications. However, many algorithms for this…
The randomized Kaczmarz methods are a popular and effective family of iterative methods for solving large-scale linear systems of equations, which have also been applied to linear feasibility problems. In this work, we propose a new block…