Three-dimensional quantum wavelet transforms

doi:10.1007/s11704-022-1639-y

Frontiers of Computer Science

2023, Vol. 17

Issue (5): 175905 https://doi.org/10.1007/s11704-022-1639-y

本期目录

Three-dimensional quantum wavelet transforms

Haisheng LI(

), Guiqiong LI(

), Haiying XIA(

)

College of Electronic and Information Engineering, Guangxi Normal University, Guilin 541004, China

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Abstract：

Wavelet transform is being widely used in the field of information processing. One-dimension and two-dimension quantum wavelet transforms have been investigated as important tool algorithms. However, three-dimensional quantum wavelet transforms have not been reported. This paper proposes a multi-level three-dimensional quantum wavelet transform theory to implement the wavelet transform for quantum videos. Then, we construct the iterative formulas for the multi-level three-dimensional Haar and Daubechies D4 quantum wavelet transforms, respectively. Next, we design quantum circuits of the two wavelet transforms using iterative methods. Complexity analysis shows that the proposed wavelet transforms offer exponential speed-up over their classical counterparts. Finally, the proposed quantum wavelet transforms are selected to realize quantum video compression as a primary application. Simulation results reveal that the proposed wavelet transforms have better compression performance for quantum videos than two-dimension quantum wavelet transforms.

Key words： wavelet transform wavelet video coding quantum wavelet transform quantum information processing quantum image processing

收稿日期: 2021-11-11 出版日期: 2022-12-29

Corresponding Author(s): Haisheng LI

引用本文:

. [J]. Frontiers of Computer Science, 2023, 17(5): 175905.
Haisheng LI, Guiqiong LI, Haiying XIA. Three-dimensional quantum wavelet transforms. Front. Comput. Sci., 2023, 17(5): 175905.

链接本文:

https://academic.hep.com.cn/fcs/CN/10.1007/s11704-022-1639-y
https://academic.hep.com.cn/fcs/CN/Y2023/V17/I5/175905

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Level	$n o r m (V 1 ? W 1)$	$n o r m (V 2 ? Λ 26, 26, 25)$	$n o r m (V 3 ? W 3)$	$n o r m (V 4 ? Λ 26, 26, 25)$
1	$7 × 10 ? 12$	$3.3 × 10 ? 11$	$3.19 × 10 ? 9$	$3.47 × 10 ? 11$
2	$3.2 × 10 ? 11$	$5.9 × 10 ? 11$	$5.72 × 10 ? 9$	$8.16 × 10 ? 11$
3	$4.05 × 10 ? 10$	$3.34 × 10 ? 10$	$8.24 × 10 ? 9$	$2.371 × 10 ? 10$
4	$1.527 × 10 ? 9$	$1.636 × 10 ? 9$	$1.238 × 10 ? 8$	$5.515 × 10 ? 10$
5	$7.746 × 10 ? 9$	$7.876 × 10 ? 9$	?	?

Tab.1

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QWTs	3D-HQWT	2D-HQWT	3D-D4QWT	2D-D4QWT
PSNR	30.39	30.40	30.14	30.81
QCR	29.08	12.94	22.06	11.61
Threshold	$λ 6 H$	$β 4 H$	$λ 1 D$	$β 2 D$
Level	5	5	4	4

Tab.2

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