Vlasov’s work<ref name="Vlasov Quantum 2003">{{cite journal|last1=Vlasov|first1=A.Y.|date=|year=1997|title=Quantum computations and images recognition|url=|journal=|volume=|pages=|arxiv=quant-ph/9703010|yearvia=2003 |last1=Vlasov |first1=A.Y.}}</ref> in 1997 focused on the use of a quantum system to recognize orthogonal images. This was followed by efforts using quantum algorithms to search specific patterns in binary images<ref name="Schutzhold Pattern 2003">{{cite journal |title=Pattern recognition on a quantum computer |journal=Physical Review A |volume=67 |issue=6 |pages=062311 |year=2003 |last1=Schutzhold |first1=R.}}</ref> and detect the posture of certain targets.<ref name="Beach Quantum 2003">{{cite journal |title=Quantum image processing (QuIP) |journal=Proceedings of the 32nd Applied Imagery Pattern Recognition Workshop |pages=39–40 |year=2003 |last1=Beach |first1=G.|last2=Lomont |first2=C.|last3=Cohen |first3=C.}}</ref> Notably, more optics-based interpretation for quantum imaging were initially experimentally demonstrated in <ref>{{cite journal |title=Optical imaging by means of two-photon quantum entanglement |journal=Physical Review A |volume=52 |issue=5 |pages=R3429-R3432 |year=1995 |last1=Pittman |first1=T.B.|last2=Shih |first2=Y.H.|last3=Strekalov |first3=D.V.}}</ref> and formalized in <ref name="Lugiato quantum 2002">{{cite journal |title=Quantum imaging |journal=Journal of Optics B |volume=4 |issue=3 |pages=S176-S183 |year=2002 |last1=Lugiato |first1=L.A.|last2=Gatti |first2=A.|last3=Brambilla |first3=E.}}</ref> after seven years. Venegas-Andraca and Bose’s Qubit Lattice<ref name="Venegas Storing 2003">{{cite journal |title=Storing, processing, and retrieving an image using quantum mechanics |journal=Proceedings of SPIE Conference of Quantum Information and Computation |pages=134–147 |year=2003 |last1=Venegas-Andraca |first1=S.E.|last2=Bose |first2=S.}}</ref> describes quantum images in 2003. Following this, Lattorre proposed another kind of representation, called the Real Ket,<ref name="Latorre Image 2005">{{cite journal |title=Image compression and entanglement |arxiv=quant-ph/0510031 |year=2005 |last1=Latorre |first1=J.I.}}</ref> whose purpose was to encode quantum images as a basis for further applications in QIMP.
Technically, these pioneering efforts with the subsequent studies related to them can be classified into three main groups:<ref name="Yan Quantum 2017"/>
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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>. Several commonly used two-dimensional image 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|last10date=Luo|first10=Zhihuang|last11=Zheng|first11=Wenqiang|last12=Li|first12=Jianzhong|last13=Zhao|first13=Meisheng|last14=Peng|first14=Xinhua|last15=Suter|first15=Dieter11 September 2017|title=Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment|url=https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.031041|journal=Physical Review X|date=11 September 2017|volume=7|issue=3|page=031041|doi=10.1103/PhysRevX.7.031041|urllast10=https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.031041Luo|first10=Zhihuang|last11=Zheng|first11=Wenqiang|last12=Li|first12=Jianzhong|last13=Zhao|first13=Meisheng|last14=Peng|first14=Xinhua|last15=Suter|first15=Dieter}} [[File:CC-BY iconBY_icon.svg|50px50x50px]] Material was copied from this source, which is available under a [https[creativecommons://creativecommons.org/licenses/by/4.0/|Creative Commons Attribution 4.0 International License]].</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.
