Related papers: Quantum Random Feature Method for Solving Partial …

Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…

This work introduces a novel method for embedding continuous variables into quantum circuits via piecewise polynomial features, utilizing low-rank tensor networks. Our approach, termed Piecewise Polynomial Tensor Network Quantum Feature…

Generative modeling has seen a rising interest in both classical and quantum machine learning, and it represents a promising candidate to obtain a practical quantum advantage in the near term. In this study, we build over a proposed…

In scientific computing, the formulation of numerical discretisations of partial differential equations (PDEs) as untrained convolutional layers within Convolutional Neural Networks (CNNs), referred to by some as Neural Physics, has…

Ridge regression (RR) is an important machine learning technique which introduces a regularization hyperparameter $\alpha$ to ordinary multiple linear regression for analyzing data suffering from multicollinearity. In this paper, we present…

Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren…

We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…

Classification is a common task in machine learning. Random features (RFs) stand as a central technique for scalable learning algorithms based on kernel methods, and more recently proposed optimized random features, sampled depending on the…

In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…

Quantum computers promise improving machine learning. We investigated the performance of new quantum neural network designs. Quantum neural networks currently employed rely on a feature map to encode the input into a quantum state. This…

There is currently a huge effort to understand the potential and limitations of variational quantum machine learning (QML) based on the optimization of parameterized quantum circuits. Recent proposals toward dequantizing variational QML…

Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…

Accurate prediction of future loan defaults is a critical capability for financial institutions that provide lines of credit. For institutions that issue and manage extensive loan volumes, even a slight improvement in default prediction…

Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…

Quantum computing, leveraging principles of quantum mechanics, represents a transformative approach in computational methodologies, offering significant enhancements over traditional classical systems. This study tackles the complex and…

Feature selection is critical in machine learning to reduce dimensionality and improve model accuracy and efficiency. The exponential growth in feature space dimensionality for modern datasets directly results in ambiguous samples and…

The radial basis function (RBF) method is used for the numerical solution of the Poisson problem in high dimension. The approximate solution can be found by solving a large system of linear equations. Here we investigate the extent to which…

Feature selection is a common step in many ranking, classification, or prediction tasks and serves many purposes. By removing redundant or noisy features, the accuracy of ranking or classification can be improved and the computational cost…

The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to…