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Anais de XXXV Simpósio Brasileiro de Telecomunicações e Processamento de Sinais

Simulação da Transformada Quântica de Fourier

Francisco Pereira, Elloá B. Guedes, Francisco de Assis

Published Jan 1, 2013• 0 citations
Publisher

Abstract

The quantum Fourier Transform is an important algorithm in Quantum Information Theory due to its capabilities to solve some Quantum Computation and Communication problems.However, so far, no practical quantum computer has been build neither its simulation is efficient on classical computers.Given these difficulties, this paper presents a software able to simulate the quantum Fourier transform -called FTSimulatorand also an analysis of its time performance.

DOI
10.14209/sbrt.2013.211

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The quantum Fourier Transform is an important algorithm in Quantum Information Theory due to its capabilities to solve some Quantum Computation and Communication problems.However, so far, no practical quantum computer has been build neither its simulation is efficient on classical computers.Given these difficulties, this paper presents a software able to simulate the quantum Fourier transform -called FTSimulatorand also an analysis of its time performance.
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A computação quântica vem sendo amplamente estudada ao longo dos últimos anos. A mesma vem mostrando-se uma tecnologia bastante promissora para o desenvolvimento da computação. Este trabalho tem como objetivo falar sobre os conceitos envolvidos para a realização da computação quântica. Para tal, foi realizada uma revisão da literatura existente sobre o tema afim de se obter o conhecimento desenvolvido sobre o mesmo até o momento. Fala-se sobre os q-bits, que é a unidade fundamental de informação da computação quântica, e suas propriedades. Em seguida são apresentadas algumas das portas lógicas quânticas que são fundamentais para a realização da computação. É apresentada uma breve introdução sobre a Transformada Quântica de Fourier (TQF) e sua forma de cálculo para um vetor ket. É apresentado o simulador de circuitos quânticos Zeno e a simulação do algoritmo da DFT, bem como possibilidade implementação de outros algoritmos no mesmo.
For discussing the solving methods of NP problems in classical computers and studying the circuit model which is the most representative in quantum computing to simulate the compute processes, this article discussed how to simulate the quantum Fourier transform by using the quantum logic gates, implemented the quantum Fourier transform and constructed the quantum information and compute simulation platform. The experiment introduced the quantum register structure to be the storage medium, which is better than the form of matrix in space. The operation processes adopted the bit manipulation to avoid the mass time for matrix multiplications. The results presented the changes of quantum amplitudes and probabilities of quantum states according to the quantum effect and compared with the approximate quantum Fourier transform. The experimental platform provided a groundwork for the further simulations of other important quantum algorithms and quantum circuits.
In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.
The Quantum Fourier Transform (QFT) has an important role in some of the most interesting and useful quantum algorithms, such as those for period finding, order finding, phase estimation and factoring. Most of the research carried out on the QFT has been developed using software simulators, however these do not emulate efficiently the quantum parallelism present in the quantum algorithms. Addressing this problem, this paper presents the hardware design of an emulator for computing the QFT using FPGAs. This emulator was designed considering a modular philosophy and it is expected to be a powerful tool to evaluate quantum algorithms that include a many-qubit QFT.