Related papers: A general quantum matrix exponential dimensionalit…

Deep learning using neural networks is an effective technique for generating models of complex data. However, training such models can be expensive when networks have large model capacity resulting from a large number of layers and nodes.…

At present, in the face of the huge and complex data in cloud computing, the parallel computing ability of quantum computing is particularly important. Quantum principal component analysis algorithm is used as a method of quantum state…

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…

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…

The reduced density matrix (RDM) plays a key role in quantum entanglement and measurement, as it allows the extraction of almost all physical quantities related to the reduced degrees of freedom. However, restricted by the degrees of…

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…

High-dimensional (HD) entanglement promises both enhanced key rates and overcoming obstacles faced by modern-day quantum communication. However, modern convex optimization-based security arguments are limited by computational constraints;…

In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…

In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging…

Deep learning is mainly based on utilizing gradient-based optimization for training Deep Neural Network (DNN) models. Although robust and widely used, gradient-based optimization algorithms are prone to getting stuck in local minima. In…

Quantile regression (QR) can be used to describe the comprehensive relationship between a response and predictors. Prior domain knowledge and assumptions in application are usually formulated as constraints of parameters to improve the…

Parallelization framework has become a necessity to speed up the training of deep neural networks (DNN) recently. Such framework typically employs the Model Average approach, denoted as MA-DNN, in which parallel workers conduct respective…

The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…

Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…

Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…

In this article, we present a novel approach for block-structured adaptive mesh refinement (AMR) that is suitable for extreme-scale parallelism. All data structures are designed such that the size of the meta data in each distributed…

In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. We demonstrate that these two algorithms have an exponential speedup over their…

Quantum machine learning (QML) is emerging as an application of quantum computing with the potential to deliver quantum advantage, but its realisation for practical applications remains impeded by challenges. Amongst those, a key barrier is…

This study proposes an automated data mining framework based on autoencoders and experimentally verifies its effectiveness in feature extraction and data dimensionality reduction. Through the encoding-decoding structure, the autoencoder can…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…