Quantum Wavelet Transform Algorithm Design And Application Research

Quantum computing is a recently developed subject crossed by math,physics and computer science. Depending on recent twenty years research, Swift and violent development has been gotten in it's extension and meaning. Quantum computing's characters and functions have being found and transformed to its'quickly developing power.The research of quantum computing mainly focus on two directions:one side, based on basic quantum mechanics'theories, a lot of quantum algorithms have been designed,which including the important large prime factorization algorithm (Shor algorithm),the unstructured database search algorithm (Grover algorithm) and many algorithms about simulating quantum system;on the other side,based on different ways of quantum computing's establishment,a number of experimental schemes have been proposed which could support the execution of these algorithms, moving quantum computation from the realm of speculation to reality.With gradual deeper research,wavelet transforms have been widely used in signal analysis and image processing area. Wavelet transforms in quantum computing area have been recongnized gradually.In the beginning of this paper, the algorithms of quantum Haar wavelet and quantum Daubechies-D(4) wavelet transform are introduced, which are based on the quantum Fourier transform.Then quantum wavelet transforms'logical factorization are proposed by use multiple-quantum operator algebra and density matrix transform theory .Thirdly,we use Mathematical to simulate the quantum wavelet transform and establish its'applications in signal analysis and image processing.Finally,Combining with the research circumstance of quantum computer and quantum programming language,we describe quantum wavelet transform algorithms and its'application ways by Q-language which are based on theQRAM( Quantum Random Access Module).Chapter 1: we introduce the history of quantum computing and its status today, and describe the method, content and meaning of our research.Chapter 2: we summarize quantum computing. From several aspects, such as qubits, quantum logic gates and parallel computing etc.Chapter 3: we introduce the quantum wavelet Haar transform algorithms in detail, give the further decomposition of quantum Haar Wavelet transform and it's complexity,and analy the processing of transform.Chapter 4: we introduce the quantum wavelet Daubechies-D(4) transform algorithms in detail, give the further decomposition of quantum D(4) Wavelet transform and it's complexity, and analy the processing of transform.Chapter 5: we use the Mathematical6.0 software to simulate two quantum wavelet transform algorithms and its'applications in signal analysis.Chapter 6: Combining with the research circumstance of quantum computer architecture and quantum programming language,we describe quantum wavelet transform algorithms and its'application ways by Q-language which are based on the QRAM( Quantum Random Access Module).Chapter 7: Summarize and forecast the quantum computing.