A New Trend of Quantum Image Representations

Quantum image processing will be an important issue in the age of quantum computers. Quantum image processing generally includes quantum image representations, quantum image processing algorithms, and quantum image measurement. Among them, quantum image representation is a very important part of quantum image processing. Therefore, it is of great significance for quantum image processing to study the representation of quantum images. First, we elaborate on the main quantum image representations and analyze, compare and summarize them. This paper focuses on the definition of these quantum image representations the preparation of quantum images and the number of quantum bits required as well as the computational complexity. Then, this paper analyzes, compares and summarizes the similarities and differences between these quantum image representations. Finally, the challenges and future development in the field of quantum image processing are summarized and forecasted. This work will help researchers to understand the advances related to quantum image representations in the field of quantum image processing and is therefore of some reference value.

[1]  P. Benjamin Dixon,et al.  Quantum Imaging and Information , 2011 .

[2]  Xiaojun Wang,et al.  Matrix Coding-Based Quantum Image Steganography Algorithm , 2019, IEEE Access.

[3]  Haiying Xia,et al.  A Quantum Image Representation Based on Bitplanes , 2018, IEEE Access.

[4]  Yu Cheng,et al.  Quantum image scaling based on bilinear interpolation with arbitrary scaling ratio , 2019, Quantum Information Processing.

[5]  Haiying Xia,et al.  Quantum vision representations and multi-dimensional quantum transforms , 2019, Inf. Sci..

[6]  Vijayan K. Asari,et al.  3D Object Classification in Uncalibrated Structure from Motion Models , 2015 .

[7]  Bing Wang,et al.  Quantum circuit design for several morphological image processing methods , 2019, Quantum Inf. Process..

[8]  N. Lindner,et al.  Topological Quantum Computation—From Basic Concepts to First Experiments , 2013, Science.

[9]  GuangZhong Liu,et al.  Detection of steganography in quantum grayscale images , 2020, Quantum Information Processing.

[10]  A. Shields.  Semiconductor quantum light sources , 2007, 0704.0403.

[11]  D. E. Savage,et al.  A programmable two-qubit quantum processor in silicon , 2017, Nature.

[12]  Xiaotong Wang,et al.  Order-encoded quantum image model and parallel histogram specification , 2019, Quantum Information Processing.

[13]  Sougato Bose,et al.  Storing, processing, and retrieving an image using quantum mechanics , 2003, SPIE Defense + Commercial Sensing.

[14]  G. Guo,et al.  Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space , 2015, Scientific Reports.

[15]  J. P. Dehollain,et al.  A two-qubit logic gate in silicon , 2014, Nature.

[16]  Rabia Amin Khan,et al.  An improved flexible representation of quantum images , 2019, Quantum Inf. Process..

[17]  Ping Fan,et al.  Quantum Implementation Circuits of Quantum Signal Representation and Type Conversion , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Naya Nagy,et al.  Image processing: why quantum? , 2020, Quantum Inf. Comput..

[19]  J. P. Dehollain,et al.  Storing quantum information for 30 seconds in a nanoelectronic device. , 2014, Nature nanotechnology.

[20]  Salvador Elías Venegas-Andraca,et al.  Discrete quantum walks and quantum image processing , 2005 .

[21]  Yuan Luo,et al.  Quantum Image Edge Detection Algorithm , 2019, International Journal of Theoretical Physics.

[22]  Chien-Yuan Chen,et al.  Information hiding method based on quantum image by using Bell states , 2019, Quantum Information Processing.

[23]  HaiSheng Li,et al.  Examining Quantum Algorithms for Quantum Image Processing , 2021 .

[24]  Liying Tan,et al.  QRCI: A new quantum representation model of color digital images , 2019, Optics Communications.

[25]  Ri-Gui Zhou,et al.  Quantum Image Edge Extraction Based on Improved Sobel Operator , 2019, International Journal of Theoretical Physics.

[26]  Kaoru Hirota,et al.  A Flexible Representation and Invertible Transformations for Images on Quantum Computers , 2011 .

[27]  Deqing Sun,et al.  A Bayesian approach to adaptive video super resolution , 2011, CVPR 2011.

[28]  Jyotsna Singh,et al.  Quantum image restoration based on Hudson–Parthasarathy Schrodinger equation , 2019, Quantum Information Processing.

[29]  Haiying Xia,et al.  Efficient quantum arithmetic operation circuits for quantum image processing , 2020, Science China Physics, Mechanics & Astronomy.

[30]  N. Gershenfeld,et al.  Bulk Spin-Resonance Quantum Computation , 1997, Science.

[31]  Sos S. Agaian,et al.  New look on quantum representation of images: Fourier transform representation , 2020, Quantum Information Processing.

[32]  Fang Zhou,et al.  Implementation of one-way quantum computing with a hybrid solid-state quantum system , 2017 .

[33]  Nan Jiang,et al.  Quantum image scaling using nearest neighbor interpolation , 2015, Quantum Inf. Process..

[34]  Davide Castelvecchi,et al.  Quantum computers ready to leap out of the lab in 2017 , 2017, Nature.

[35]  C. Monroe,et al.  Scaling the Ion Trap Quantum Processor , 2013, Science.

[36]  R. Schoelkopf,et al.  Superconducting Circuits for Quantum Information: An Outlook , 2013, Science.

[37]  Aiping Lu,et al.  Design of Threshold Segmentation Method for Quantum Image , 2020 .

[38]  Xiande Liu,et al.  Color image representation model and its application based on an improved FRQI , 2017 .

[39]  Frank Y. Shih,et al.  Image Processing and Pattern Recognition: Fundamentals and Techniques , 2010 .

[41]  Ahmed El-Rafei,et al.  Similarity assessment of quantum images , 2019, Quantum Inf. Process..

[42]  Yu Cheng,et al.  Quantum image edge extraction based on improved Prewitt operator , 2019, Quantum Information Processing.

[43]  Mark Saffman,et al.  Quantum computing with neutral atoms , 2017, National science review.

[45]  Kai Lu,et al.  An Optimized Quantum Representation for Color Digital Images , 2018, International Journal of Theoretical Physics.

[46]  V. Manta,et al.  Image processing using quantum computing , 2012, 2012 16th International Conference on System Theory, Control and Computing (ICSTCC).

[47]  Kai Lu,et al.  NEQR: a novel enhanced quantum representation of digital images , 2013, Quantum Information Processing.

[48]  Shuxiang Song,et al.  A Block-Based Quantum Image Scrambling for GNEQR , 2019, IEEE Access.

[49]  Simona Caraiman,et al.  Image Representation and Processing Using Ternary Quantum Computing , 2013, ICANNGA.

[50]  Fei Yan,et al.  An RGB Multi-Channel Representation for Images on Quantum Computers , 2013, J. Adv. Comput. Intell. Intell. Informatics.

[51]  Fei Yan,et al.  A survey of quantum image representations , 2015, Quantum Information Processing.

[52]  Zhenxing He,et al.  Quantum image processing algorithm using edge extraction based on Kirsch operator. , 2020, Optics express.

[53]  Ri-Gui Zhou,et al.  Efficient quantum steganography scheme using inverted pattern approach , 2019, Quantum Inf. Process..

[54]  Qingxin Zhu,et al.  Image storage, retrieval, compression and segmentation in a quantum system , 2013, Quantum Inf. Process..

[55]  Jing Ma,et al.  Double quantum color images encryption scheme based on DQRCI , 2019, Multimedia Tools and Applications.

[56]  Qiong Li,et al.  A novel quantum representation of color digital images , 2017, Quantum Inf. Process..

[57]  She-Xiang Jiang,et al.  Improved Quantum Image Median Filtering in the Spatial Domain , 2019, International Journal of Theoretical Physics.

[58]  Bing Wang,et al.  Quantum implementation of classical Marr–Hildreth edge detection , 2020, Quantum Inf. Process..

[59]  Lijiang Chen,et al.  SQR: a simple quantum representation of infrared images , 2014, Quantum Information Processing.

[60]  Mario Mastriani.  Quantum image processing: the pros and cons of the techniques for the internal representation of the image. A reply to: A comment on “Quantum image processing?” , 2020, Quantum Inf. Process..

[61]  Ihsan Yilmaz,et al.  QRMW: Quantum representation of multi wavelength images , 2018, Turkish J. Electr. Eng. Comput. Sci..

[62]  Salvador E. Venegas-Andraca,et al.  Region-based approach for the spectral clustering Nyström approximation with an application to burn depth assessment , 2015, Machine Vision and Applications.

[63]  She-Xiang Jiang,et al.  Quantum image sharpness estimation based on the Laplacian operator , 2020 .

[64]  Yaron Silberberg,et al.  Super-resolution enhancement by quantum image scanning microscopy , 2018, Nature Photonics.

[65]  Andrew Steane,et al.  Fast quantum logic gates with trapped-ion qubits , 2017, Nature.

[66]  E. Charbon,et al.  Quantum correlation measurement with single photon avalanche diode arrays. , 2019, Optics express.

[67]  Gang Xu,et al.  Quantum Image Steganography Protocol Based on Quantum Image Expansion and Grover Search Algorithm , 2019, IEEE Access.

[68]  V. V.D. Shah.  Image Processing and its Military Applications , 1987 .

[69]  Marco Lanzagorta,et al.  Quantum Radar , 2011, Quantum Radar.

[70]  Xingyu Yan,et al.  Multi-image encryption scheme based on quantum 3D Arnold transform and scaled Zhongtang chaotic system , 2018, Quantum Information Processing.

[71]  Kaoru Hirota,et al.  A flexible representation of quantum images for polynomial preparation, image compression, and processing operations , 2011, Quantum Inf. Process..

[72]  D. Okada,et al.  Digital Image Processing for Medical Applications , 2009 .

[73]  Bing Wang,et al.  Quantum Representation of Indexed Images and its Applications , 2020 .

[74]  Abdullah M. Iliyasu.  Towards Realising Secure and Efficient Image and Video Processing Applications on Quantum Computers , 2013, Entropy.

[75]  Kai Xu,et al.  A novel quantum representation for log-polar images , 2013, Quantum Information Processing.

[76]  Fei Yan,et al.  Hybrid Quantum-Classical Protocol for Storage and Retrieval of Discrete-Valued Information , 2014, Entropy.

[77]  Yi-Xian Yang,et al.  A quantum image dual-scrambling encryption scheme based on random permutation , 2019, Science China Information Sciences.

[78]  M. Lukin,et al.  Probing many-body dynamics on a 51-atom quantum simulator , 2017, Nature.

[79]  Qingxin Zhu,et al.  Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state , 2014, Quantum Inf. Process..

[80]  Di Xiao,et al.  Quantum Block Image Encryption Based on Arnold Transform and Sine Chaotification Model , 2019, IEEE Access.

[81]  Ahmed Farouk,et al.  Red-Green-Blue multi-channel quantum representation of digital images , 2017 .