相关论文: Randomized Householder QR

In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while…

All-photonic quantum repeaters use multi-qubit photonic graph states, called repeater graph states (RGS), instead of matter-based quantum memories, for protection against predominantly loss errors. The RGS comprises tree-graph-encoded…

Quantum algorithms typically demand prohibitively complicated circuits to solve practical problems. Previous studies have shown that classical randomness can accelerate some specific quantum algorithms. In this work, we introduce the…

As Computed Tomography (CT) scans are an essential medical test, many techniques have been proposed to reconstruct high-quality images using a smaller amount of radiation. One approach is to employ algebraic factorization methods to…

This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…

Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…

With the rising popularity of intelligent mobile devices, it is of great practical significance to develop accurate, realtime and energy-efficient image Super-Resolution (SR) inference methods. A prevailing method for improving the…

We introduce the first randomized algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework for many quantum algorithms. Standard implementations of QSVT rely on block encodings of the Hamiltonian, which are costly…

Linear Regression is a seminal technique in statistics and machine learning, where the objective is to build linear predictive models between a response (i.e., dependent) variable and one or more predictor (i.e., independent) variables. In…

We develop a randomized Newton method capable of solving learning problems with huge dimensional feature spaces, which is a common setting in applications such as medical imaging, genomics and seismology. Our method leverages randomized…

We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…

Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the…

The high overhead of fault-tolerant measurement sequences (FTMSs) poses a major challenge for implementing quantum stabilizer codes. Here, we address this problem by constructing efficient FTMSs for the class of quantum Hamming codes…

Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing interest in…

We present an implementation of Pagh's compressed matrix multiplication algorithm, a randomized algorithm that constructs sketches of matrices to compute an unbiased estimate of their product. By leveraging fast polynomial multiplication…

We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the…

In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…

We consider a one-parameter family of piecewise isometries of a rhombus. The rotational component is fixed, and its coefficients belong to the quadratic number field $K=\mathbb{Q}(\sqrt{2})$. The translations depend on a parameter $s$ which…

Recently, supervised hashing methods have attracted much attention since they can optimize retrieval speed and storage cost while preserving semantic information. Because hashing codes learning is NP-hard, many methods resort to some form…

Randomized protocols are procedures that incorporate probabilistic choices during their execution and they play a central role in quantum algorithms, spanning Hamiltonian simulation, noise mitigation, and measurement tasks. In practical…