相关论文: Quantum mean centering for block-encoding-based qu…

Machine-learning tasks frequently involve problems of manipulating and classifying large numbers of vectors in high-dimensional spaces. Classical algorithms for solving such problems typically take time polynomial in the number of vectors…

Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…

Accurate and efficient prediction of electronic wavefunctions is central to ab initio molecular dynamics (AIMD) and electronic structure theory. However, conventional ab initio methods require self-consistent optimization of electronic…

The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…

Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…

In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a…

Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…

We propose a new clustering algorithm that is robust to the presence of outliers in the dataset. We perform Lloyd-type iterations with robust estimates of the centroids. More precisely, we build on the idea of median-of-means statistics to…

Quantum computers progress toward outperforming classical supercomputers, but quantum errors remain their primary obstacle. The key to overcoming errors on near-term devices has emerged through the field of quantum error mitigation,…

Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario,…

In large-scale statistical modeling, reducing data size through subsampling is essential for balancing computational efficiency and statistical accuracy. We propose a new method, Principal Component Analysis guided Quantile Sampling…

A task-based formulation of Scalable Universal Matrix Multiplication Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is applied to the multiplication of hierarchy-free, rank-structured matrices that appear in the…

Quantum linear system solvers like the Quantum Singular Value Transformation (QSVT) require a block encoding of the system matrix $A$ within a unitary operator $U_A$. Unfortunately, block encoding often results in significant…

Quantization-Aware Training (QAT) has driven much attention to produce efficient neural networks. Current QAT still obtains inferior performances compared with the Full Precision (FP) counterpart. In this work, we argue that quantization…

The LINPACK benchmark reports the performance of a computer for solving a system of linear equations with dense random matrices. Although this task was not designed with a real application directly in mind, the LINPACK benchmark has been…

Block-encoding operators are one of the essential components in quantum algorithms based on Quantum Signal Processing. Their gate complexity largely determines the overall gate complexity of the full algorithm. Using variational methods, we…

Variational Quantum Circuits (VQC) lie at the forefront of quantum machine learning research. Still, the use of quantum networks for real data processing remains challenging as the number of available qubits cannot accommodate a large…

Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…

Over half a century old and showing no signs of aging, k-means remains one of the most popular data processing algorithms. As is well-known, a proper initialization of k-means is crucial for obtaining a good final solution. The recently…

In the rapidly evolving research on artificial intelligence (AI) the demand for fast, computationally efficient, and scalable solutions has increased in recent years. The problem of optimizing the computing resources for distributed machine…