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Advances in the Quantum Theoretical Approach.pdf


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Advances in the Quantum Theoretical Approach to Image Processing Applications

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communities worldwide and led to a flurry of interest from both academia and industrial stakeholders in quantum computer science. The culmination of this interest
was the announcement in 2007 that D-wave, a Canadian technology company, had
developed a commercially available quantum computer, albeit the fact that this firstgeneration quantum computer is analogous to the room-size ENIAC computer of the
1940s. However, it is not a general-purpose quantum computer. Rather, it is a quantum annealer that was developed to solve optimization problems. Nonetheless, this
quantum machine was acquired by Lockheed Martin in 2011 and then by a consortium
of Google and NASA in 2013. The goal of the latter acquisition is to use the D-wave
quantum machine as a launch pad of an indigenous effort by Google scientists to create
a quantum computer but with significantly advanced features than those of the Dwave machine, such as multifunctionality. Even though quantum computers and their
first-generation realizations have shown promising results, it is important to note that
in some cases, quantum algorithms are not superior in performance to their classical
counterparts. An example of such cases is mentioned in Fijany and Williams [1998].
Quantum computational models for several information-theoretic constructs, such
as image processing and big data analysis [Mastriani 2014a], have shown promise
of enhanced results in computational efficiency. Big data refers to extremely large
datasets that could be analyzed to reveal certain patterns or draw conclusions and
associations. This takes an extensive amount of calculations since the size of data is
significantly large. Big data clustering and classification algorithms have been proposed
to run on quantum computers as well as for topological data analysis [Lloyd et al. 2016].
In case of the latter, the quantum algorithm for identifying the topological shape of the
data performs dramatically faster than the corresponding classical algorithms. For
instance, if there exists a space with n points and k scales, performing the classical
persistent homology takes as much time as O(22n). On the other hand, the quantum
algorithm takes as much time as O(n5 ) [Lloyd et al. 2016].
Images are one form that big data can take. Image processing has been studied extensively on classical computers beginning from image acquisition to image analysis
dealing with enhancement, segmentation, transformations, and security. The use of
quantum computation within the context of visual signal processing can potentially
allow the handling of millions of visual signals simultaneously using the quantum
mechanical principle of superposition (discussed in more detail in Section 2), without
compromise in the computational demand [Dubey et al. 2014]. In particular, quantum
models of image processing through modifications to existing classical techniques can
dramatically improve the results of several image processing tasks in terms of speed
and performance [Dubey et al. 2014], independent of the image size. Despite such overwhelming attention to quantum image processing (QuIP) in the recent years, one main
challenge that remains is finding quantum algorithms that characterize images better and faster than their classical counterparts [Mastriani 2014a]. However, the first
steps taken toward exploring the possibility of manipulating image pixels as quantum states have made the field of QuIP quite promising. This has primarily involved
major improvements in hardware, such as the development and use of quantum computers [Beach et al. 2003]; however, without the development of compatible software
techniques, accomplishing real-world use could become a daunting task.
Some initial research has been conducted in quantum image storage, retrieval, and
compression [Li et al. 2013a, 2014; Venegas-Andraca and Ball 2010; Zhang et al. 2013c;
Vlasov 1997; Beach et al. 2003; Venegas-Andraca 2003a, 2003b; Latorre 2005; Le et al.
2010; Yan et al. 2015a; Iliyasu et al. 2011]. Most of the researchers have approached
these areas by exploiting the principles of quantum superposition and quantum entanglement that will be discussed in Section 2. Briefly, quantum superpositions are
joint states of many quantum systems. Mathematically, the Cartesian product is the
“standard” way to create a composite system from given individual systems. However,
ACM Computing Surveys, Vol. 49, No. 4, Article 75, Publication date: February 2017.