Related papers: Multidimensional Quantum Fourier Transformation
The non-equidistant fast Fourier transform (NFFT) is an extension of the famous fast Fourier transform (FFT), which can be applied to non-equidistantly sampled data in time/space or frequency domain. It is an approximative algorithm that…
Consider the following generalized hidden shift problem: given a function f on {0,...,M-1} x Z_N satisfying f(b,x)=f(b+1,x+s) for b=0,1,...,M-2, find the unknown shift s in Z_N. For M=N, this problem is an instance of the abelian hidden…
A kind of brand-new robot, quantum robot, is proposed through fusing quantum theory with robot technology. Quantum robot is essentially a complex quantum system and it is generally composed of three fundamental parts: MQCU (multi quantum…
Fourier transformations of pseudo-Boolean functions are popular tools for analyzing functions of binary sequences. Real-world functions often have structures that manifest in a sparse Fourier transform, and previous works have shown that…
The developments of quantum computing algorithms and experiments for atomic scale simulations have largely focused on quantum chemistry for molecules, while their application in condensed matter systems is scarcely explored. Here we present…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
We propose a novel scheme to implement the BB84 quantum key distribution (QKD) protocol in optical fibers based on a quantum frequency-translation (QFT) process. Unlike conventional QKD systems, which rely on photon polarization/phase to…
Although many of works have been done in multivalued quantum logic synthesis, the question whether multivalued quantum circuits are more efficient than the conventional binary quantum circuits is still open. In this article we devote to the…
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm.…
The quantum Fourier transform (QFT) is a ubiquitous quantum operation that is used in numerous quantum computing applications. The major obstacle to constructing a QFT circuit is that numerous elementary gates are required. Among the…
The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially…
We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on…
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental…
Contemporary quantum computers encode and process quantum information in binary qubits (d = 2). However, many architectures include higher energy levels that are left as unused computational resources. We demonstrate a superconducting…
In this study, we present a technique based on the quantum Fourier transform (QFT) that allows the generation of disjoint sets of entangled particles, in such a way that particles of the same set are entangled with each other, while…
We will present a few new generalizations of the multi-controlled X (MCX) gate that uses the quantum Fourier transform (QFT). Firstly, we will optimize QFT-MCX and prove that it is equivalent to a stair MCX gates array. This stair-wise…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
Using the circulant symmetry of a Hamiltonian describing three qubits, we realize the quantum Fourier transform. This symmetry allows us to construct a set of eigenvectors independently on the magnitude of physical parameters involved in…
Algorithms for processing data in short-time batches are critical for both online and offline processing of streamed and large data respectively due to the quadratic relation between signal length and computational cost of convolution-based…
Fast Fourier Transforms (FFT) are widely used to reduce memory and computational costs in deep learning. However, existing implementations, including standard FFT and real FFT (rFFT), cannot achieve true in-place computation. In particular,…