The aim of this work is to give an introduction for a non-practical reader to the growing field
of quantum machine learning, which is a recent discipline that combines the research areas …

Differential equations are the foundation of mathematical models representing the universe's
physics. Hence, it is significant to solve partial and ordinary differential equations, such as …

Parametric quantum circuits play a crucial role in the performance of many variational
quantum algorithms. To successfully implement such algorithms, one must design efficient …

Generative machine learning methods such as large-language models are revolutionizing
the creation of text and images. While these models are powerful they also harness a large …

One of the challenges in quantum computing is the synthesis of unitary operators into
quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries …

Neighborhood preserving embedding (NPE) is an important linear dimensionality reduction
technique that aims at preserving the local manifold structure. NPE contains three steps, ie …

Inspired by random walks on graphs, the diffusion map (DM) is a class of unsupervised
machine learning that offers automatic identification of low-dimensional data structure …

Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as
matrices with structures generalizing these types are omnipresent in computations of …

Partial differential equations frequently appear in the natural sciences and related
disciplines. In this work, we explore the potential for enhancing a classical deep-learning …

Quantum computing offers a promising new avenue for advancing computational methods in
science and engineering. In this work, we introduce the quantum asymptotic numerical …