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{{Short description|Processing quantum-encoded images}}
'''Quantum image processing (QIMP)''' is using [[quantum computing]] or [[quantum information processing]] to create and work with [[quantum image]]s.<ref name="Venegas-Andraca2005">{{cite thesis |last= Venegas-Andraca |first= Salvador E.|date= 2005 |title= Discrete Quantum Walks and Quantum Image Processing|type= DPhil thesis|publisher= The University of Oxford|url= https://ora.ox.ac.uk/objects/uuid:2baab08b-ee68-4ce5-8e68-8201f086a1ba}}</ref><ref name="Iliyasu Towards 2013">{{cite journal |title=Towards realising secure and efficient image and video processing applications on quantum computers |journal=Entropy |volume=15 |issue=8 |pages=2874–2974 |year=2013 |last1=Iliyasu |first1=A.M.|bibcode=2013Entrp..15.2874I |doi=10.3390/e15082874 |doi-access=free }}</ref>
Due to some of the properties inherent to quantum computation, notably [[Quantum entanglement|entanglement]] and [[Parallel computing|parallelism]], it is hoped that QIMP technologies will offer capabilities and performances that surpass their traditional equivalents, in terms of computing speed, security, and minimum storage requirements.<ref name="Iliyasu Towards 2013" /><ref name="Yan Quantum 2017">{{cite journal |title=Quantum image processing: A review of advances in its security technologies |journal=International Journal of Quantum Information |volume=15 |issue=3 |pages=1730001–44 |year=2017 |last1=Yan |first1=F.|last2=Iliyasu |first2=A.M.|last3=Le |first3=P.Q.|doi=10.1142/S0219749917300017 |bibcode=2017IJQI...1530001Y |doi-access=free }}</ref>
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==Background==
A. Y. Vlasov's work<ref name="Vlasov Quantum 2003">{{cite journal|last1=Vlasov|first1=A.Y.|year=1997|title=Quantum computations and images recognition|url=https://archive.org/details/arxiv-quant-ph9703010|arxiv=quant-ph/9703010|bibcode=1997quant.ph..3010V}}</ref> in 1997 focused on the use of a quantum system to recognize [[Orthogonality|orthogonal]] images. This was followed by efforts using [[quantum algorithms]] to search specific patterns in [[binary image]]s<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.|arxiv=quant-ph/0208063 |doi=10.1103/PhysRevA.67.062311 |bibcode=2003PhRvA..67f2311S }}</ref> and detect the posture of certain targets.<ref name="Beach Quantum 2003">{{cite book |pages=39–40 |year=2003 |last1=Beach |first1=G.|last2=Lomont |first2=C.|last3=Cohen |first3=C.
In 2003, Salvador Venegas-Andraca and S. Bose presented Qubit Lattice, the first published general model for storing, processing and retrieving images using quantum systems.<ref name="Venegas-AndracaIJCAI2003">{{cite journal |title=Quantum Computation and Image Processing: New Trends in Artificial Intelligence |journal=Proceedings of the 2003 IJCAI International Conference on Artificial Intelligence |pages=1563–1564 |year=2003 |last1=Venegas-Andraca |first1=S.E.|last2=Bose|first2=S.|url=https://www.ijcai.org/Proceedings/03/Papers/276.pdf}}</ref><ref name="Venegas Storing 2003">{{cite book |journal=Proceedings of SPIE Conference of Quantum Information and Computation |volume=5105 |pages=134–147 |year=2003 |last1=Venegas-Andraca |first1=S.E.|last2=Bose |first2=S.|title=Quantum Information and Computation |chapter=Storing, processing, and retrieving an image using quantum mechanics |editor3-first=Howard E |editor3-last=Brandt |editor2-first=Andrew R |editor2-last=Pirich |editor1-first=Eric |editor1-last=Donkor |bibcode=2003SPIE.5105..137V |doi=10.1117/12.485960 |s2cid=120495441 }}</ref> Later on, in 2005, Latorre proposed another kind of representation, called the Real Ket,<ref name="Latorre Image 2005">{{cite journal |title=Image compression and entanglement |url=https://archive.org/details/arxiv-quant-ph0510031 |arxiv=quant-ph/0510031 |year=2005 |last1=Latorre |first1=J.I.|bibcode=2005quant.ph.10031L }}</ref> whose purpose was to encode quantum images as a basis for further applications in QIMP. Furthermore, in 2010 Venegas-Andraca and Ball presented a method for storing and retrieving [[Well-known text representation of geometry|binary geometrical shapes]] in quantum mechanical systems in which it is shown that maximally entangled [[
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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==Quantum image manipulations==
A lot of the effort in QIMP has been focused on designing [[
To illustrate the feasibility and capability of QIMP algorithms and application, researchers always prefer to simulate the digital image processing tasks on the basis of the QIRs that we already have. By using the basic quantum gates and the aforementioned operations, so far, researchers have contributed to quantum image feature extraction,<ref name="Zhang Local 2015">{{cite journal |title= Local feature point extraction for quantum images |journal= Quantum Information Processing |volume=14 |issue=5 |pages=1573–1588 |year=2015 |last1=Zhang |first1=Y. |last2=Lu |first2=K. |last3= Xu |first3=K. |last4= Gao |first4=Y. |last5= Wilson |first5=R. |doi= 10.1007/s11128-014-0842-7 |bibcode= 2015QuIP...14.1573Z |s2cid= 20213446 }}</ref> quantum [[image segmentation]],<ref name="Caraiman Histogram 2014">{{cite journal |title= Histogram-based segmentation of quantum images |journal= Theoretical Computer Science |volume=529 |pages=46–60 |year=2014 |last1=Caraiman |first1=S. |last2=Manta |first2=V. |doi= 10.1016/j.tcs.2013.08.005 |doi-access=free }}</ref> quantum image morphology,<ref name="Yuan Quantum 2015">{{cite journal |title= Quantum morphology operations based on quantum representation model |journal= Quantum Information Processing |volume=14 |issue=5 |pages=1625–1645 |year=2015 |last1=Yuan |first1=S. |last2=Mao |first2=X. |last3= Li |first3=T. |last4= Xue |first4=Y. |last5= Chen |first5=L. |last6= Xiong |first6=Q.|doi= 10.1007/s11128-014-0862-3 |bibcode= 2015QuIP...14.1625Y |s2cid= 44828546 }}</ref> quantum image comparison,<ref name="Yan A 2013">{{cite journal |title= A parallel comparison of multiple pairs of images on quantum computers |journal= International Journal of Innovative Computing and Applications |volume=5 |issue=4 |pages=199–212 |year=2013 |last1=Yan |first1=F. |last2=Iliyasu |first2=A. |last3= Le |first3=P. |last4= Sun |first4=B. |last5= Dong |first5=F. |last6= Hirota |first6=K.|doi= 10.1504/IJICA.2013.062955 }}</ref> quantum image filtering,<ref name="Caraiman Quantum 2013">{{cite journal |title= Quantum image filtering in the frequency ___domain |journal= Advances in Electrical and Computer Engineering |volume=13 |issue=3 |pages=77–84 |year=2013 |last1=Caraiman |first1=S. |last2=Manta |first2=V. |doi= 10.4316/AECE.2013.03013 |doi-access=free }}</ref> quantum image classification,<ref name="Ruan Quantum 2016">{{cite journal |title= Quantum computation for large-scale image classification |journal= Quantum Information Processing |volume=15 |issue=10|pages=4049–4069 |year=2016 |last1=Ruan |first1=Y. |last2=Chen |first2=H. |last3= Tan |first3=J. |url=https://www.researchgate.net/publication/305644388|doi= 10.1007/s11128-016-1391-z |bibcode= 2016QuIP...15.4049R |s2cid= 27476075 }}</ref> quantum [[image stabilization]],<ref name="Yan Strategy 2016">{{cite journal |title= Strategy for quantum image stabilization |journal= Science China Information Sciences |volume=59 |issue= 5 |pages=052102 |year=2016 |last1=Yan |first1=F. |last2=Iliyasu |first2=A. |last3= Yang |first3=H. |last4= Hirota |first4=K. |doi= 10.1007/s11432-016-5541-9 |s2cid= 255200782 |doi-access= }}</ref> among others. In particular, QIMP-based security technologies have attracted extensive interest of researchers as presented in the ensuing discussions. Similarly, these advancements have led to many applications in the areas of [[
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 mechanics|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 an 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 transform|Fourier]], [[Hadamard transform|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 name="2017_Yao" /> 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.
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