相关论文: A presentation of the quantum Fourier transform fr…
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 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 a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that…
The algorithm behind the Fast Fourier Transform has a simple yet beautiful geometric interpretation that is often lost in translation in a classroom. This article provides a visual perspective which aims to capture the essence of it.
Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…
We present the detailed process of converting the classical Fourier Transform algorithm into the quantum one by using QR decomposition. This provides an example of a technique for building quantum algorithms using classical ones. The…
This paper is an essentially self-contained and rigorous description of the fundamental principles of quantum computing from a mathematical perspective. It is intended to help mathematicians who want to get a grasp of this quickly growing…
There are many falsely intuitive introductions to quantum theory and quantum computation in a handwave. There are also numerous documents which teach those subjects in a mathematically sound manner. To my knowledge this paper is the…
The proposed framework represents the first tool to compile a quantum circuit across photonic-connected distributed quantum processors. Its design follows a divide-and-conquer paradigm for circuit partitioning, transpilation, and assembly,…
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
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…
Quantum systems have an exponentially large degree of freedom in the number of particles and hence provide a rich dynamics that could not be simulated on conventional computers. Quantum reservoir computing is an approach to use such a…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…