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In general, the work pursued by the researchers in this area are focused on expanding the applicability of QIMP to realize more classical-like digital image processing algorithms; propose technologies to physically realize the QIMP hardware; or simply to note the likely challenges that could impede the realization of some QIMP protocols.
==Quantum image transform==
By encoding and processing the image information in quantum-mechanical systems, a framework of quantum image processing is presented, where a pure quantum state encodes the image information: to encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states.
Given a image <math>F=(F_{i,j})_{M \times L}</math>, where <math>F_{i,j}</math> represents the pixel value at position <math>(i,j)</math> with <math>i = 1,\dots,M</math> and <math>j = 1,\dots,L</math>, a vector <math>\vec{f}</math> with <math>ML</math> elements can be formed by letting the first <math>M</math> elements of <math>\vec{f}</math> be the first column of <math>F</math>, the next <math>M</math> elements the second column, etc.
A large class of image operations is linear, e.g., unitary transformations, convolutions, and linear filtering.
In the quantum computing, the linear transformation can be represented as <math>|g\rangle =\hat{U} |f\rangle </math> with the input image state <math>|f\rangle </math> and the output image state <math>|g\rangle </math>. A unitary transformation can be implemented as a unitary evolution.
Some basic and commonly used image transforms (e.g., the Fourier, Hadamard, and Haar wavelet transforms) can be expressed in the form <math>G=PFQ</math>, with the resulting image <math>G</math> and a row (column) transform matrix <math> P (Q)</math>. The corresponding unitary operator <math>\hat{U}</math> can then be written as <math> \hat{U}={Q}^T \otimes {P}</math>. for quantum image are imple
Several commonly used two-dimensional transforms, such as the Haar wavelet, Fourier, and Hadamard transforms,are experimentally demonstrated on a quantum computer<ref>{{cite journal|last1=Yao|first1=Xi-Wei|last2=Wang|first2=Hengyan|last3=Liao|first3=Zeyang|last4=Chen|first4=Ming-Cheng|last5=Pan|first5=Jian|last6=Li|first6=Jun|last7=Zhang|first7=Kechao|last8=Lin|first8=Xingcheng|last9=Wang|first9=Zhehui|last10=Luo|first10=Zhihuang|last11=Zheng|first11=Wenqiang|last12=Li|first12=Jianzhong|last13=Zhao|first13=Meisheng|last14=Peng|first14=Xinhua|last15=Suter|first15=Dieter|title=Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment|journal=Physical Review X|date=11 September 2017|volume=7|issue=3|page=031041|doi=10.1103/PhysRevX.7.031041|url=https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.031041}}</ref>, with exponential speedup over their classical counterparts. In addition, a novel highly efficient quantum algorithm is proposed and experimentally implemented for detecting the boundary between different regions of a picture: It requires only one single-qubit gate in the processing stage, independent of the size of the picture.
==References==
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