Related papers: Kernel $k$-Medoids as General Vector Quantization

Quantum Kernel Estimation (QKE) is a technique based on leveraging a quantum computer to estimate a kernel function that is classically difficult to calculate, which is then used by a classical computer for training a Support Vector Machine…

Quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (QA). We present a…

Hypergraph partitioning is a fundamental optimization problem with applications in data management and other domains involving higher-order relations. In this paper, we study balanced hypergraph partitioning from the perspective of quantum…

The evolution of multiple-input, multiple-output (MIMO) systems requires the efficient detection algorithms to overcome the exponential computational complexity of optimal maximum likelihood detection. Reformulating MIMO detection as a…

The reconstruction of trajectories of charged particles is a key computational challenge for current and future collider experiments. Considering the rapid progress in quantum computing, it is crucial to explore its potential for this and…

Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…

Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a…

Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic…

This paper addresses the Quadratic Multiple Constraints Variable-Sized Bin Packing Problem (QMC-VSBPP), a challenging combinatorial optimization problem that generalizes the classical bin packing problem by incorporating multiple capacity…

Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of…

The prospect of quantum solutions for complicated optimization problems is contingent on mapping the original problem onto a tractable quantum energy landscape, e.g. an Ising-type Hamiltonian. Subsequently, techniques like adiabatic…

This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent advances regarding confidence bands and geometric/topological features. We begin with a discussion of basic properties of KDE: the convergence rate…

Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the…

Quantum machine learning (QML) is the spearhead of quantum computer applications. In particular, quantum neural networks (QNN) are actively studied as the method that works both in near-term quantum computers and fault-tolerant quantum…

The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles…

An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…

We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are…

The feature vector mapping used to represent chemical systems is a key factor governing the superior data-efficiency of kernel based quantum machine learning (QML) models applicable throughout chemical compound space. Unfortunately, the…

Given is a set of images, where all images show views of the same area at different points in time and from different viewpoints. The task is the alignment of all images such that relevant information, e.g., poses, changes, and terrain, can…