Related papers: Generalized tensor transforms and their applicatio…

Fast Fourier Transform (FFT) is one of the most important tools in digital signal processing. FFT costs O(N \log N) for transforming a signal of length N. Recently, Sparse Fourier Transform (SFT) has emerged as a critical issue addressing…

Hybrid Tensor Networks (hTN) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. However, their practical usefulness and many…

In the Quantum-Train (QT) framework, mapping quantum state measurements to classical neural network weights is a critical challenge that affects the scalability and efficiency of hybrid quantum-classical models. The traditional QT framework…

The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this…

Using quantum algorithms to simulate complex physical processes and correlations in quantum matter has been a major direction of quantum computing research, towards the promise of a quantum advantage over classical approaches. In this work…

Graph Neural Networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum Computing (QC) offers a…

In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…

A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…

The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…

We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…

The main approach to hybrid quantum-classical neural networks (QNN) is employing quantum computing to build a neural network (NN) that has quantum features, which is then optimized classically. Here, we propose a different strategy: to use…

We found that the actual computational time-cost of the QFT is O(n 2^n) for large n in a quantum computer using nuclear spins. The computational cost of a quantum algorithm has usually been estimated as the sum of the universal gates…

Transformers serve as the backbone architectures of Foundational Models, where domain-specific tokenizers allow them to adapt to various domains. Graph Transformers (GTs) have recently emerged as leading models in geometric deep learning,…

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…

Tensor computations, with matrix multiplication being the primary operation, serve as the fundamental basis for data analysis, physics, machine learning, and deep learning. As the scale and complexity of data continue to grow rapidly, the…

Quantum computation represents a promising frontier in the domain of high-performance computing, blending quantum information theory with practical applications to overcome the limitations of classical computation. This study investigates…

Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)} (r^2) r^{l} Y_{lm}(\vartheta,\varphi)$, $|m| \leq l < n \in \mathbb{N}$, $L_{n-l-1}^{(l + 1/2)}$ being a generalized Laguerre…

Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…

The Number Theoretic Transform (NTT) is an indispensable tool for computing efficient polynomial multiplications in post-quantum lattice-based cryptography. It has strong resemblance with the Fast Fourier Transform (FFT), which is the most…

By the newly developed technique of integration within an ordered product (IWOP) of operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier…