Advances in the Quantum Theoretical Approach.pdf
N. Abura’ed et al.
other products, such as the tensor product, are also possible. In quantum physics, the
tensor product is a more general construction allowing for the production of joint states
that are correlated more strongly than states in any classical physical system. These
latter joint quantum states are said to be entangled and are the source of enhanced
results observed in quantum information processing. Baez  provides an excellent discussion on the way the tensor product makes quantum physics dramatically
different from classical physics.
There are also other lines of research that involve denoising [Pan et al. 2012; Brida
et al. 2010; Mastriani 2014a; Bhattacharyya et al. 2014; Yuan et al. 2013; Wang and Li
2007; Zhou et al. 2010; Fu et al. 2010] and edge detection [Zhang et al. 2012; Dubey et al.
2014; Yi et al. 2014], in addition to preliminary research that has been accomplished in
pseudocoloring, which is a branch of image enhancement [Jiang et al. 2015]. Some of
these explorations mainly aim to extend the classical, well-known techniques into the
quantum domain—for example, the median filter [Yuan et al. 2013; Zhou et al. 2010].
The main feature common to both noise and the quantum representation of bits is that
both of them are probabilistic in nature—that is, both the quantum measurement of
qubits (explained further in Section 2) and noise intensity can be modeled as a probability distribution. Hence, the filters that have been extended to the quantum domain
appear more adaptive to the noise intensity because a pixel can have different possible
states depending on the noise intensity (see Section 4 for more details). In addition,
there have been initial studies conducted in image watermarking [Zhang et al. 2013b;
Yang et al. 2013a; Song et al. 2013; Yang et al. 2014; Song et al. 2014a; Soliman et al.
2015; Iliyasu et al. 2012; Iliyasu 2013] that aim to enhance image security without
distorting it or degrading its quality. Furthermore, preliminary research has been conducted for image understanding and transformations on quantum computers [Le et al.
2010, 2011c; Wang et al. 2015a; Jiang and Wang 2015; Yan et al. 2012a; Yan et al. 2012b;
Zhou and Sun 2015; Yuan et al. 2014a; Zhou et al. 2015b; Caraiman and Manta 2009].
This article sheds light on some of the important QuIP techniques and their relevant applications. We also compare these quantum formulations to their classical
counterparts using performance metrics such as the signal-to-noise ratio (SNR), peak
signal-to-noise ratio (PSNR), and mean squared error (MSE). Some of the main novelty
and contributions of this survey include:
—Detailed insights into the applications of quantum computing to image processing.
—Qualitative and quantitative comparison of existing QuIP techniques and their classical counterparts.
—A critical review of the advances and trends in image processing.
—A statistical summary of the studied techniques to draw recommendations for future
work in this area.
The remainder of the article is organized as follows. A brief introduction to quantum
information and computation is provided in Section 2. Further, the survey will review
image processing techniques and their respective quantum equivalent techniques for
image storage, retrieval, and compression in Section 3; image enhancement through
denoising in Section 4; edge detection in Section 5; image understanding and computer
vision in Section 6; image transformations in Section 7; and image security using digital
watermarking, encryption, and scrambling in Section 8. Recommendations and possible
future work for QuIP will be presented along with indicative quantitative results and
a statistical summary of the literature in Section 9. We conclude in Section 10.
2. FUNDAMENTALS OF QUANTUM INFORMATION AND COMPUTING
Advances in computation technology over the past two decades have roughly followed
Moore’s law, which asserts that the number of transistors on a microprocessor doubles approximately every 2 years [Moore 1965]. Extrapolating this trend, somewhere
ACM Computing Surveys, Vol. 49, No. 4, Article 75, Publication date: February 2017.