Quantum image processing: Difference between revisions

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{{Underlinked|date=March 2019}}

'''Quantum image processing''' (QIP) is primarily devoted to using quantum computing and quantum information processing to create and work with quantum images.<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 }}</ref> Due to some of the astounding properties inherent to quantum computation, notably entanglement and parallelism, it is anticipated that QIP technologies will offer capabilities and performances that are, as yet, unrivaled by their traditional equivalents. These improvements could be in terms of computing speed, guaranteed security, and minimal storage requirements, etc.<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=17300011730001–44 |year=2017 |last1=Yan |first1=F.|last2=Iliyasu |first2=A.M.|last3=Le |first3=P.Q.|url=https://www.worldscientific.com/doi/pdfplus/=10.1142/S0219749917300017 |bibcode=2017IJQI...1530001Y }}</ref>

==Background==

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|via=|bibcode=1997quant.ph..3010V}}</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.|urlarxiv=https://arxiv.org/pdf/quant-ph/0208063 |arxivdoi=quant-ph10.1103/0208063PhysRevA.67.062311 }}</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.|doi=10.1109/AIPR.2003.1284246 |isbn=0-7695-2029-4 }}</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-R3432R3429–R3432 |year=1995 |last1=Pittman |first1=T.B.|last2=Shih |first2=Y.H.|last3=Strekalov |first3=D.V.|bibcode=1995PhRvA..52.3429P |doi=10.1103/PhysRevA.52.R3429 |pmid=9912767 }}</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-S183S176–S183 |year=2002 |last1=Lugiato |first1=L.A.|last2=Gatti |first2=A.|last3=Brambilla |first3=E.|doi=10.1088/1464-4266/4/3/372 |bibcode=2002JOptB...4S.176L |arxiv=quant-ph/0203046 }}</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 |volume=5105 |pages=134–147 |year=2003 |last1=Venegas-Andraca |first1=S.E.|last2=Bose |first2=S.|bibcode=2003SPIE.5105..137V |doi=10.1117/12.485960 |series=Quantum Information and Computation }}</ref> describes quantum images in 2003. Simultaneously, 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.|bibcode=2005quant.ph.10031L }}</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"/>

#Quantum-assisted digital image processing (QDIP): These applications aim at improving digital or classical image processing tasks and applications.<ref name="Iliyasu Towards 2013"/>

#Optics-based quantum imaging (OQI)<ref name="Pittman Optical 1995">{{cite journal |title=Quantum imaging|journal= Progress in Optics |volume=51 |issue=7 |pages=251–348 |year=2008 |last1=Gatti |first1=A. |last2=Brambilla |first2=E. |doi= 10.1016/S0079-6638(07)51005-X }}</ref>

#Classically-inspired quantum image processing (QIP)<ref name="Iliyasu Towards 2013"/>

==Quantum image manipulations==

A lot of the effort in QIP has been focused on designing algorithms to manipulate the position and color information encoded using the FRQI and its many variants. For instance, FRQI-based fast geometric transformations including (two-point) swapping, flip, (orthogonal) rotations<ref name="Le Fast 2010">{{cite journal |title= Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state |journal= IAENG International Journal of Applied Mathematics |volume=40 |issue=3 |pages=113–123 |year=2010 |last1=Le |first1=P. |last2=Iliyasu |first2=A. |last3= Dong |first3=F. |last4= Hirota |first4=K. }}</ref> and restricted geometric transformations to constrain these operations to a specified area of an image<ref name="Le Strategies 2011">{{cite journal |title= Strategies for designing geometric transformations on quantum images |journal= Theoretical Computer Science |volume=412 |issue=15 |pages=1406–1418 |year=2011 |last1=Le |first1=P. |last2=Iliyasu |first2=A. |last3= Dong |first3=F. |last4= Hirota |first4=K. |url=https://core.ac.uk/download/pdf/82724999.pdf|doi= 10.1016/j.tcs.2010.11.029 }}</ref> were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image<ref name="Wang Quantum 2015">{{cite journal |title= Quantum image translation |journal= Quantum Information Processing |volume=14 |issue=5 |pages=1589–1604 |year=2015 |last1=Wang |first1=J. |last2=Jiang |first2=N. |last3= Wang |first3=L. |doi= 10.1007/s11128-014-0843-6 |bibcode= 2015QuIP...14.1589W }}</ref> and quantum image scaling to resize a quantum image<ref name="Jiang Quantum 2015">{{cite journal |title= Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio |journal= Quantum Information Processing |volume=14 |issue=11 |pages=4001–4026 |year=2015 |last1=Jiang |first1=N. |last2=Wang |first2=J. |last3= Mu |first3=Y. |doi= 10.1007/s11128-015-1099-5 |bibcode= 2015QuIP...14.4001J }}</ref> were discussed. While FRQI-based general form of color transformations were first proposed by means of the single qubit gates such as X, Z, and H gates.<ref>{{cite journal |title= Efficient colour transformations on quantum image |journal= Journal of Advanced Computational Intelligence and Intelligent Informatics |volume=15 |issue=6 |pages=698–706 |year=2011 |last1=Le |first1=P. |last2= Iliyasu |first2=A. |last3= Dong |first3=F. |last4= Hirota |first4=K. |doi= 10.20965/jaciii.2011.p0698 }}</ref> Later, MCQI-based channel of interest (CoI) operator to entail shifting the grayscale value of the preselected color channel and the channel swapping (CS) operator to swap the grayscale values between two channels were fully discussed in.<ref name="Sun Multi 2014">{{cite journal |title= Multi-channel information operations on quantum images |journal= Journal of Advanced Computational Intelligence and Intelligent Informatics |volume=18 |issue=2 |pages=140–149 |year=2014 |last1=Sun |first1=B. |last2=Iliyasu |first2=A. |last3= Yan |first3=F. |last4= Garcia |first4=J. |last5= Dong |first5=F. |last6= Al-Asmari |first6=A.|doi= 10.20965/jaciii.2014.p0140 }}</ref>

To illustrate the feasibility and capability of QIP 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 }}</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 }}</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 }}</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 }}</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/profile/Xi_Li95/publication/305644388_Quantum_computation_for_large-scale_image_classification305644388|doi= 10.1007/links/5a2f4804aca2726d0bd6c420/Quantums11128-computation016-for1391-large-scale-image-classificationz |bibcode= 2016QuIP.pdf..15.4049R }}</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 }}</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 watermarking,<ref name="Iliyasu Watermarking 2012">{{cite journal |title= Watermarking and authentication of quantum images based on restricted geometric transformations |journal= Information Sciences |volume=186 |issue=1|pages=126–149 |year=2012 |last1=Iliyasu |first1=A. |last2=Le |first2=P. |last3= Dong |first3=F. |last4= Hirota |first4=K. |doi= 10.1016/j.ins.2011.09.028 }}</ref><ref name="Heidari Watermarking 2016">{{cite journal |title= A Novel Lsb based Quantum Watermarking |journal= International Journal of Theoretical Physics |volume= 55 |issue=10 |pages=4205–4218 |year=2016|last1=Heidari |first1=S. |last2=Naseri |first2=M. |doi= 10.1007/s10773-016-3046-3 |bibcode= 2016IJTP...55.4205H }}</ref><ref>{{cite journal |title= A quantum watermark protocol |journal= International Journal of Theoretical Physics |volume=52 |issue=2|pages=504–513 |year=2013 |last1=Zhang |first1=W. |last2=Gao |first2=F. |last3= Liu |first3=B. |last4= Jia |first4=H. |bibcode=2013IJTP...52..504Z |doi=10.1007/s10773-012-1354-9 }}</ref> encryption,<ref name="Zhou Quantum 2013">{{cite journal |title= Quantum image encryption and decryption algorithms based on quantum image geometric transformations. International |journal= Journal of Theoretical Physics |volume=52 |issue=6|pages=1802–1817 |year=2013 |last1=Zhou |first1=R. |last2=Wu |first2=Q. |last3= Zhang |first3=M. |last4= Shen |first4=C. |doi= 10.1007/s10773-012-1274-8 }}</ref> and steganography<ref name="Jiang Lsb 2015">{{cite journal |title= Lsb based quantum image steganography algorithm |journal= International Journal of Theoretical Physics |volume=55 |issue=1|pages=107–123 |year=2015 |last1=Jiang |first1=N. |last2=Zhao |first2=N. |last3= Wang |first3=L. |doi= 10.1007/s10773-015-2640-0 }}</ref> etc., which form the core security technologies highlighted in this area.

In general, the work pursued by the researchers in this area are focused on expanding the applicability of QIP 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.

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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|date=11 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|volume=7|issue=3|page=031041|doi=10.1103/PhysRevX.7.031041|last10=Luo|first10=Zhihuang|last11=Zheng|first11=Wenqiang|last12=Li|first12=Jianzhong|last13=Zhao|first13=Meisheng|last14=Peng|first14=Xinhua|last15=Suter|first15=Dieter|arxiv=1801.01465|bibcode=2017PhRvX...7c1041Y}} [[File:CC-BY_icon.svg|50x50px]] Material was copied from this source, which is available under a [[creativecommons: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.

==References==