Related papers: A CS guide to the quantum singular value transform…
In this work, a novel quantum neural network is introduced as a means to approximate any unitary evolution through the Standard Recursive Block Basis (SRBB) and is subsequently redesigned with the number of CNOTs asymptotically reduced by…
In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (R3SVD) algorithm is used to adaptively carry out partial…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
In this paper, we explore the power of Quantum Machine Learning as we extend, implement and evaluate algorithms like Quantum Support Vector Classifier (QSVC), Pegasos-QSVC, Variational Quantum Circuits (VQC), and Quantum Neural Networks…
In high-dimensional data processing and data analysis related to dual quaternion statistics, generalized singular value decomposition (GSVD) of a dual quaternion matrix pair is an essential numerical linear algebra tool for an elegant…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…
The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on $\mathrm{SU}(1,1)$ has been widely studied, its $\mathrm{SU}(2)$ variant has only recently…
We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…
Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion…
This paper introduces quantum circuit methodologies for pointwise multiplication and convolution of complex functions, conceptualized as "processing through encoding". Leveraging known techniques, we describe an approach where multiple…
We present a scalable algorithm for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities on a fault-tolerant universal quantum computer. As a proof of concept of our quantum…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains…
Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
Quantum signal processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciated challenge is that all systematic…
In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-form), to the study of quantum machine learning algorithms and derive general results that are applicable to a variety of input models,…
Quantum simulation of chemical Hamiltonians enables the efficient calculation of chemical properties. Mapping is one of the essential steps in simulating fermionic systems on quantum computers. In this work, a unified framework of…