Related papers: Quantum K-medians Algorithm Using Parallel Euclide…

Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…

We devise new quantum algorithms that exponentially speeds up the training and prediction procedures of twin support vector machines (TSVM). To train TSVMs using quantum methods, we demonstrate how to prepare the desired input states…

K-means (MacQueen, 1967) [1] is one of the simplest unsupervised learning algorithms that solve the well-known clustering problem. The procedure follows a simple and easy way to classify a given data set to a predefined, say K number of…

$k$-means clustering is NP-hard in the worst case but previous work has shown efficient algorithms assuming the optimal $k$-means clusters are \emph{stable} under additive or multiplicative perturbation of data. This has two caveats. First,…

Quantum computing (QC) seems to show potential for application in machine learning (ML). In particular quantum kernel methods (QKM) exhibit promising properties for use in supervised ML tasks. However, a major disadvantage of kernel methods…

Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…

Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…

One of the applications of center-based clustering algorithms such as K-Means is partitioning data points into K clusters. In some examples, the feature space relates to the underlying problem we are trying to solve, and sometimes we can…

Quantum machine learning promises to efficiently solve important problems. There are two persistent challenges in classical machine learning: the lack of labeled data, and the limit of computational power. We propose a novel framework that…

Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems, which demonstrates to be able to explore the most relevant portion of the exponentially large quantum Hilbert space…

The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…

Clustering algorithms are a cornerstone of machine learning applications. Recently, a quantum algorithm for clustering based on the k-means algorithm has been proposed by Kerenidis, Landman, Luongo and Prakash. Based on their work, we…

We design new differentially private algorithms for the Euclidean k-means problem, both in the centralized model and in the local model of differential privacy. In both models, our algorithms achieve significantly improved error guarantees…

Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…

Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative…

The anticlustering problem is to partition a set of objects into K equal-sized anticlusters such that the sum of distances within anticlusters is maximized. The anticlustering problem is NP-hard. We focus on anticlustering in Euclidean…

One of the simplest and most effective classical machine learning algorithms is the $k$-nearest neighbors algorithm ($k$NN) which classifies an unknown test state by finding the $k$ nearest neighbors from a set of $M$ train states. Here we…

This paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm. Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced…

Big data mining is well known to be an important task for data science, because it can provide useful observations and new knowledge hidden in given large datasets. Proximity-based data analysis is particularly utilized in many real-life…

Quantum machine learning consists in taking advantage of quantum computations to generate classical data. A potential application of quantum machine learning is to harness the power of quantum computers for generating classical data, a…