Related papers: A Polylogarithmic-Time Quantum Algorithm for the L…

Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…

We propose a quantum analogue of Bluestein's algorithm (QBA) that implements an exact $N$-point Quantum Fourier Transform (QFT) for arbitrary $N$. Our construction factors the $N$-dimensional QFT unitary into three diagonal quadratic-phase…

We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…

We propose an implementation of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform occurs naturally in the unitary time evolution of energy eigenstates and is used to define an…

The quantum Fourier transform (QFT) is a fundamental primitive in quantum computation and quantum information. In this work, we generalize the QFT for finite groups to a QFT for finite-dimensional semisimple algebras, and give efficient…

In this paper, an algorithm for Quantum Inverse Fast Fourier Transform (QIFFT) is developed to work for quantum data. Analogous to a classical discrete signal, a quantum signal can be represented in Dirac notation, application of QIFFT is a…

- In this paper we present a method to compute the coefficients of the fractional Fourier transform (FrFT) on a quantum computer using quantum gates of polynomial complexity of the order O(n^3). The FrFt, a generalization of the DFT, has…

We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…

The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a…

The advent of fault-tolerant quantum computers marks a significant milestone, yet the development of practical quantum algorithms remains a critical challenge. Effective quantum algorithms are essential for leveraging the power of quantum…

We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…

We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector…

The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…

As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…

Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…

This study examines the potential for fault-tolerant quantum computers to provide utility in fluid dynamics simulations, with a focus on drag force calculations for ship hull design. We assess whether quantum algorithms can surpass…

We construct a quantum algorithm that creates the Laughlin state for an arbitrary number of particles $n$ in the case of filling fraction one. This quantum circuit is efficient since it only uses $n(n-1)/2$ local qudit gates and its depth…

Few of the known quantum algorithms can be reliably executed on a quantum computer. Therefore, as an extension, we propose a Parallel Quantum Hough transform (PQHT) algorithm that we execute on a quantum computer. We give its implementation…

Quantum computing hardware is undergoing rapid development from proof-of-principle devices to scalable machines that could eventually challenge classical supercomputers on specific tasks. On platforms with local connectivity, the transition…

This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…