Approximate quantum Fourier transform and decoherence

Approximate quantum Fourier transform and decoherence.

We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive approximations can be made before the accuracy of AQFT (as compared with regular quantum Fourier transform) is compromised. We show that for some computations an...

Coping with Decoherence: Parallelizing the Quantum Fourier Transform

Rank-varying computational complexity describes those computations in which the complexity of executing each step is not a constant, but evolves throughout the computation as a function of the order of execution of each step [2]. This paper identi es a practical instance of this computational paradigm in the procedure for inverting the quantum Fourier transform. It is shown herein that under th...

An Approximate Fourier Transform Useful in Quantum Factoring

Wavelet transform based fast approximate Fourier transform

We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coe cients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational comple...

Fast Approximate Fourier Transform via Wavelets Transform

We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coeecients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational comple...