Related papers: Sublinear Time Quantum Sensitivity Sampling

Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and…

We study efficient algorithms for the Euclidean $k$-Center problem, focusing on the regime of large $k$. We take the approach of data reduction by considering $\alpha$-coreset, which is a small subset $S$ of the dataset $P$ such that any…

A \emph{strong coreset} for the mean queries of a set $P$ in ${\mathbb{R}}^d$ is a small weighted subset $C\subseteq P$, which provably approximates its sum of squared distances to any center (point) $x\in {\mathbb{R}}^d$. A \emph{weak…

Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…

Image classification is a core task of intelligent sensing, conventionally follows a sequential imaging then processing pipeline. However, redundant high-dimensional image reconstruction is inherently inefficient, especially in photon…

Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…

Maximizing the computational utility of near-term quantum processors requires predictive noise models that inform robust, noise-aware compilation and error mitigation. Conventional models often fail to capture the complex error dynamics of…

We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…

The theoretical framework for networked quantum sensing has been developed to a great extent in the past few years, but there are still a number of open questions. Among these, a problem of great significance, both fundamentally and for…

Supervised learning under measurement constraints is a common challenge in statistical and machine learning. In many applications, despite extensive design points, acquiring responses for all points is often impractical due to resource…

The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…

We consider quantile estimation in a semi-supervised setting, characterized by two available data sets: (i) a small or moderate sized labeled data set containing observations for a response and a set of possibly high dimensional covariates,…

Recent experimental breakthroughs have signalled the imminent arrival of the early fault-tolerant era. However, for a considerable period in the foreseeable future, relying solely on quantum error correction for full error suppression will…

Although linear quantum amplification has proven essential to the processing of weak quantum signals, extracting higher-order quantum features such as correlations in principle demands nonlinear operations. However, nonlinear processing of…

The problem of approximately computing the $k$ dominant Fourier coefficients of a vector $X$ quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT…

Quantum algorithms designed for realistic quantum many-body systems, such as chemistry and materials, usually require a large number of measurements of the Hamiltonian. Exploiting different ideas, such as {importance sampling,} observable…

We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…

Demonstration of quantum advantage for classical machine learning tasks remains a central goal for quantum technologies and artificial intelligence. Two major bottlenecks to this goal are the high dimensionality of practical datasets and…

It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For…

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated…