Related papers: A presentation of the quantum Fourier transform fr…
The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…
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…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
In this work, we describe examples for calculating the 1-D circular convolution of signals represented by 3-qubit superpositions. The case is considered, when the discrete Fourier transform of one of the signals is known and calculated in…
With the race to build large-scale quantum computers and efforts to exploit quantum algorithms for efficient problem solving in science and engineering disciplines, the requirement to have efficient and scalable verification methods are of…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We study a quantum computer with fixed and permanent interaction of diagonal type between qubits. It is controlled only by one-qubit quick transformations. It is shown how to implement Quantum Fourier Transform and to solve Shroedinger…
In this paper an alternative version of the quantum phase estimation is proposed, in which the Hadamard gates at the beginning are substituted by a quantum Fourier transform. This new circuit coincides with the original one, when the…
Quantum computing is a highly abstract scientific discipline, which, however, is expected to have great practical relevance in future information technology. This forces educators to seek new methods to teach quantum computing for students…
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 development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Our primary purpose is to isolate the abstract, mathematical properties of circuits -- both classical Boolean circuits and quantum circuits -- that are essential for their computational interpretation. A secondary purpose is to clarify the…
This article defines and proves basic properties of the standard quantum circuit model of computation. The model is developed abstractly in close analogy with (classical) deterministic and probabilistic circuits, without recourse to any…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics,…
Significant efforts are being spent on building a quantum computer. At the same time, developments in quantum software are rapidly progressing. Insufficient quantum resources often are the problem when running quantum algorithms. New…
Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation were in use, based on either full…