Analysis of Five Techniques for the Internal Representation of a Digital Image Inside a Quantum Processor

In this paper, five techniques, for the representation of a digital image inside a quantum processor, are compared. The techniques are: flexible representation of quantum images (FRQI), novel enhanced quantum representation (NEQR), generalized quantum image representation (GQIR), multi-channel representation for quantum images (MCQI), and quantum Boolean image processing (QBIP). The comparison will be based on implementations on the Quirk simulator, and on the IBM Q Experience processors, from the point of view of performance, robustness (noise immunity), deterioration of the outcomes due to decoherence, and technical viability.

[1]  Ahmed El-Rafei,et al.  Quantum Image Watermarking Algorithm Based on Haar Wavelet Transform , 2019, IEEE Access.

[2]  Zhengang Jiang,et al.  Quantum Computation-Based Image Representation, Processing Operations and Their Applications , 2014, Entropy.

[3]  Robert W. Boyd,et al.  Quantum imaging technologies , 2014, 1406.1685.

[4]  Hiroshi Imai,et al.  Power, Puzzles and Properties of Entanglement , 2001, MCU.

[5]  Kai Lu,et al.  A Strategy of Quantum Image Filtering in Frequency Domain , 2017 .

[6]  Nan Jiang,et al.  Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio , 2015, Quantum Information Processing.

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

[8]  B. Saleh,et al.  Quantum image processing , 2001 .

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

[10]  Anirban Pathak,et al.  Elements of Quantum Computation and Quantum Communication , 2013 .

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

[12]  Fei Yan,et al.  Quantum Image Searching Based on Probability Distributions , 2012 .

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

[14]  Silvia Ledesma,et al.  Classical images as quantum entanglement: An image processing analogy of the GHZ experiment , 2011 .

[15]  Abdullah M. Iliyasu,et al.  Fast Geometric Transformations on Quantum Images , 2010 .

[16]  Abdullah M. Iliyasu,et al.  A Multi-Channel Representation for images on quantum computers using the RGBα color space , 2011, 2011 IEEE 7th International Symposium on Intelligent Signal Processing.

[17]  M. Schlosshauer.  Decoherence, the measurement problem, and interpretations of quantum mechanics , 2003, quant-ph/0312059.

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

[19]  D. Batens,et al.  Theory and Experiment , 1988 .

[20]  David P. DiVincenzo,et al.  Quantum Computing: A Short Course from Theory to Experiment , 2004 .

[21]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[22]  Jason W. Fleischer,et al.  Quantum Phase Imaging using Spatial Entanglement , 2015 .

[23]  E. Rieffel,et al.  Quantum Computing: A Gentle Introduction , 2011 .

[24]  Abdullah M. Iliyasu,et al.  Strategies for designing geometric transformations on quantum images , 2011, Theor. Comput. Sci..

[25]  Mario Mastriani,et al.  Quantum Image Processing: the truth, the whole truth, and nothing but the truth about its problems on internal image representation and outcomes recovering , 2020, 2002.04394.

[26]  Mario Mastriani.  Quantum Boolean image denoising , 2015, Quantum Inf. Process..

[27]  D. M. Ha,et al.  A gentle introduction , 2006 .

[28]  Nan Jiang,et al.  A Survey on Quantum Image Processing , 2018, Chinese Journal of Electronics.

[29]  Mario Mastriani.  Quantum image processing? , 2017, Quantum Inf. Process..

[30]  Nan Jiang,et al.  A Novel Quantum Image Compression Method Based on JPEG , 2017 .

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

[32]  A. John Arul.  Impossibility of comparing and sorting quantum states , 2001 .

[33]  Abdullah M. Iliyasu.  Roadmap to Talking Quantum Movies: a Contingent Inquiry , 2019, IEEE Access.

[34]  Abid Yahya,et al.  Steganography Techniques for Digital Images , 2018 .

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

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

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

[38]  H. Prakash.  Quantum teleportation , 2009, 2009 International Conference on Emerging Trends in Electronic and Photonic Devices & Systems.

[39]  E. Merzbacher.  Decoherence and the Quantum-To-Classical Transition , 2008 .

[40]  Akira Furusawa,et al.  Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing , 2011 .

[41]  Jia Luo,et al.  Traceable Quantum Steganography Scheme Based on Pixel Value Differencing , 2019, Scientific Reports.

[42]  Matt Harding,et al.  Representation of Quantum Images , 2018 .

[43]  Fei Yan,et al.  Quantum image processing: A review of advances in its security technologies , 2017 .

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

[45]  Guo-Hua Sun,et al.  Application of Flexible Presentation of Quantum Images in Multipartite Correlations , 2018 .

[46]  Mikio Nakahara,et al.  Quantum Computing - From Linear Algebra to Physical Realizations , 2008 .

[47]  Ping Fan,et al.  Quantum realization of the bilinear interpolation method for NEQR , 2017, Scientific Reports.

[48]  Raymond Laflamme,et al.  An Introduction to Quantum Computing , 2007, Quantum Inf. Comput..