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Quantum Wavelet Packet Transforms

Quantum Wavelet Packet Transforms
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Copyright: 2021
Pages: 25
Source title: Examining Quantum Algorithms for Quantum Image Processing
Source Author(s)/Editor(s): HaiSheng Li (Guangxi Normal University, China)
DOI: 10.4018/978-1-7998-3799-2.ch006


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Quantum wavelet packet transform (QWPT) may play an important role in quantum information processing. In this chapter, the authors design quantum circuits of a generalized tensor product (GTP) and a perfect shuffle permutation (PSP). Next, they propose multi-level and multi-dimensional (1D, 2D and 3D) QWPTs, including Haar QWPT (HQWPT), D4 QWPT (DQWPT) based on the periodization extension and their inverse transforms for the first time, and prove the correctness based on the GTP and PSP. Furthermore, they analyze the quantum costs and the time complexities of the proposed QWPTs and obtain precise results. The time complexities of HQWPTs is at most six basic operations on 2n elements, which illustrates high efficiency of the proposed QWPTs.

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