Complete quantum circuit of Haar wavelet based MRA

Wael Badawy

Guoling Wang, Weiqian Zhao, Ping Zou +3 more

He, Yuguo, Sun +1 more

Wavelet analysis has applications in many areas, such as signal analysis and image processing. We propose a method for generating the complete circuit of Haar wavelet based MRA by factoring butterfly matrices and conditional perfect shuffle permutation matrices. The factorization of butterfly matrices is the essential part of the design. As a result, it is the key point to obtain the circuits of .I2t()W()I2n-2t-2. In this paper, we use a simple means to develop quantum circuits for this kind of matrices. Similarly, the conditional permutation matrix is implemented entirely, combined with the scheme of Fijany and Williams. The cir-cuits and the ideas adopted in the design are simple and in-telligible.

Song Hong Yan

The Haar wavelet algorithm based on quantum computing and its application for color image compression are discussed.Firstly,classical Haar wavelet operator is decomposed into direct sums,direct products and dot products of unitary matrices,so that shuffle permutation matrices is found.Secondly,based on the generalized Kronecker product,Harr functions are decomposed into a sequence of W-H and shuffle permutation matrices.Thirdly,the efficient,complete,quantum circuits for representative quantum wavelet transform are given.Finally,algorithm for color image compression by quantum Haar wavelet is presented,and experiment results are given.The experiment results show that the quantum Haar wavelet has very good feasibility in image compression.

Zhenghan Wang

Colin P. Williams