Quantum Wavelet Transforms

2021 ◽  
pp. 193-220
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Wavelet Transform ◽  
Tensor Product ◽  
Wavelet Transforms ◽  
Quantum Information Processing ◽  
Complexity Analysis ◽  
Simulation Experiments ◽  
Multi Level

The classical wavelet transform has been widely applied in the information processing field. It implies that quantum wavelet transform (QWT) may play an important role in quantum information processing. This chapter firstly describes the iteration equations of the general QWT using generalized tensor product. Then, Haar QWT (HQWT), Daubechies D4 QWT (DQWT), and their inverse transforms are proposed respectively. Meanwhile, the circuits of the two kinds of multi-level HQWT are designed. What's more, the multi-level DQWT based on the periodization extension is implemented. The complexity analysis shows that the proposed multi-level QWTs on 2n elements can be implemented by O(n3) basic operations. Simulation experiments demonstrate that the proposed QWTs are correct and effective.

Quantum Wavelet Packet Transforms

2021 ◽  
pp. 221-245
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
High Efficiency ◽  
Quantum Information Processing ◽  
Wavelet Packet ◽  
Quantum Circuits ◽  
Multi Level ◽  
2D And 3D ◽  
First Time ◽  
Perfect Shuffle

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.

Quantum Information Processing

2001 ◽  
Author(s):  
David P. DiVincenzo ◽  
Charles H. Bennett
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing

QCCM - Center for NMR Quantum Information Processing

2011 ◽  
Author(s):  
David G. Cory ◽  
Chandrasekhar Ramanathan ◽  
Raymond Laflamme ◽  
Joseph V. Emerson ◽  
Jonathan Baugh
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing

scholarly journals An improved novel quantum image representation and its experimental test on IBM quantum experience

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jie Su ◽  
Xuchao Guo ◽  
Chengqi Liu ◽  
Shuhan Lu ◽  
Lin Li
Keyword(s):  
Image Processing ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Image Representation ◽  
Reference Value ◽  
Vertical Position ◽  
Quantum Image ◽  
Quantum Image Representation ◽  
Ibm Quantum Experience

AbstractQuantum image representation (QIR) is a necessary part of quantum image processing (QIP) and plays an important role in quantum information processing. To address the problems that NCQI cannot handle images with inconsistent horizontal and vertical position sizes and multi-channel image processing, an improved color digital image quantum representation (INCQI) model based on NCQI is proposed in this paper. The INCQI model can process color images and facilitate multi-channel quantum image transformations and transparency information processing of images using auxiliary quantum bits. In addition, the quantum image control circuit was designed based on INCQI. And quantum image preparation experiments were conducted on IBM Quantum Experience (IBMQ) to verify the feasibility and effectiveness of INCQI quantum image preparation. The prepared image information was obtained by quantum measurement in the experiment, and the visualization of quantum information was successfully realized. The research in this paper has some reference value for the research related to QIP.

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