Quantum image processing: Difference between revisions

Revision as of 23:00, 31 October 2024

Revision as of 12:53, 18 November 2024

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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 using 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.|title=32nd Applied Imagery Pattern Recognition Workshop, 2003. Proceedings. |chapter=Quantum image processing (QuIP) |doi=10.1109/AIPR.2003.1284246 |isbn=0-7695-2029-4 |s2cid=32051928 }}</ref> Notably, more optics-based interpretations 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.|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–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 |s2cid=9640455 }}</ref> after seven years.

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 [[qubit]]s can be used to reconstruct images without using any additional information.<ref name="Venegas-Andraca2010">{{cite journal |title=Processing Images in Entangled Quantum Systems |journal=Quantum Informatiom Processing |volume=9 |issue=1 |pages=1–11 |year=2010 |last1=Venegas-Andraca |first1=S.E.|last2=Ball |first2=J.|doi=10.1007/s11128-009-0123-z |bibcode=2010QuIP....9....1V |s2cid=34988263 }}</ref>

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 representations ==

There are various approaches for quantum image representation, that are usually based on the encoding of color information. A common representation is FRQI (''Flexible Representation for Quantum Images''), that captures the color and position at every pixel of the image, and defined as:<ref name=":0">{{Citation |lastlast1=Yan |firstfirst1=Fei |title=Quantum Image Representations |date=2020 |work=Quantum Image Processing |pages=19–48 |url=http://link.springer.com/10.1007/978-981-32-9331-1_2 |access-date=2024-10-31 |place=Singapore |publisher=Springer Singapore |language=en |doi=10.1007/978-981-32-9331-1_2 |isbn=978-981-329-330-4 |last2=Venegas-Andraca |first2=Salvador E.}}</ref><math display="block">\vert I \rangle = \frac{1}{2^{n}} \sum^{2^{2n-1}}_{i=0} \vert c_{i} \rangle \otimes \vert i \rangle</math>where <math display="inline">| i \rangle </math> is the position and <math display="inline">\vert c_{i} \rangle = cos \theta_{i} \vert 0 \rangle + sin \theta_{i} \vert 1 \rangle</math> the color with a vector of angles <math display="inline">\theta_{i} \in \left[0, \pi/2 \right]</math>. As it can be seen, <math display="inline">\vert c_{i} \rangle </math> is a regular [[Qubit#Qubit states|qubit state]] of the form <math>\vert \psi\rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle</math>, with basis states <math display="inline">\vert 0 \rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix}</math> and <math display="inline">\vert 1 \rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix} </math>, as well as amplitudes <math display="inline">\alpha </math> and <math display="inline">\beta </math> that satisfy <math display="inline">\left|\alpha\right|^{2} + \left|\beta\right|^{2} = 1</math>.<ref>{{Citation |lastlast1=Yan |firstfirst1=Fei |title=Introduction and Overview |date=2020 |work=Quantum Image Processing |pages=1–17 |url=http://link.springer.com/10.1007/978-981-32-9331-1_1 |access-date=2024-10-31 |place=Singapore |publisher=Springer Singapore |language=en |doi=10.1007/978-981-32-9331-1_1 |isbn=978-981-329-330-4 |last2=Venegas-Andraca |first2=Salvador E.}}</ref>

Another common representation is MCQI (''Multi-Channel Representation for Quantum Images''), that uses the [[RGB color model|RGB]] channels with quantum states and following FRQI definition:<ref name=":0" /><math display="block">\vert I\rangle = \frac{1}{2^{n+1}} \sum^{2^{2n-1}}_{i=0} \vert C^{i}_{RGB}\rangle \otimes \vert i\rangle</math><math display="block">\begin{aligned}