摘要
Wavelet analysis has applications in many ar- eas, such as signal analysis and image processing. We pro- pose a method for generating the complete circuit of Haar wavelet based MRA by factoring butterfly matrices and con- ditional perfect shuffle permutation matrices. The factoriza- tion of butterfly matrices is the essential part of the design. As a result, it is the key point to obtain the circuits of I 2t ⊕ W ⊕ I 2n ? 2t ?2. In this paper, we use a simple means to de- velop 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.
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 ＋I2^n-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 circuits and the ideas adopted in the design are simple and intelligible.
作者
HE Yuguo1,2 & SUN Jigui1,3 1. College of Computer Science and Technology, Jilin University, Changchun 130012, China
2. Department of Computer Science and Engineering, Beijing Institute of Technology, Beijing 100081, China
3. Key Laboratory of Computation and Knowledge Engineering of Min-istry of Education, Jilin University, Changchun 130012, China
基金
This work was supported by the National Natural Science Foundation of China(Grant Nos.60273080&60473003)
Natural Science Foundation of Jilin Province(Grant No.20030107).
作者简介
Correspondence should be addressed to He Yuguo （email： yuguo@bit.edu.cn）
