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arXiv:2012.11036

A Quantum Edge Detection Algorithm

Giacomo Cavalieri, Dario Maio

Published Dec 20, 2020• 6 citations
arXivHTMLPDF

Abstract

The application of quantum computing to the field of image processing has produced several promising applications: quantum image representation techniques have been developed showing how, by taking advantage of quantum properties like entanglement and superposition, many image processing algorithms could have an exponential speed-up in comparison to their "classical" counterparts. In this paper, after briefly discussing some of the main quantum image representation methods, we propose an improved version of a quantum edge detection algorithm.

DOI
10.48550/arxiv.2012.11036

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Abstract Edges are image locations where the gray value intensity changes suddenly. They are among the most important features to understand and segment an image. Edge detection is a standard task in digital image processing, solved, for example, using filtering techniques. However, the amount of data to be processed grows rapidly and pushes even supercomputers to their limits. Quantum computing promises exponentially lower memory usage in terms of the number of qubits compared to the number of classical bits. In this paper, we propose a hybrid method for quantum edge detection based on the idea of a quantum artificial neuron. Our method can be practically implemented on quantum computers, especially on those of the current noisy intermediate-scale quantum era. We compare six variants of the method to reduce the number of circuits and thus the time required for the quantum edge detection. Taking advantage of the scalability of our method, we can practically detect edges in images considerably larger than reached before.
The basics of quantum computing will be discussed. The introduction to different types of computing environments will be done. The concept of qubits will be introduced and compared with bits. The concepts of superposition and quantum entanglement will be discussed. The application of Shor’s and Grover’s algorithm will be discussed briefly and how these algorithms contribute for the enormous power of quantum computing will be elaborated. The brief description of quantum gates will be introduced. Algorithms like Quantum Hadamard Edge Detection can identify outlines and features significantly faster than classical methods will be explained. Topics on protection of visual data through quantum encryption and quantum key distribution will be explained. The pattern recognition using hybrid quantum machine learning models for image classification and segmentation will be elaborated.
Quantum Image Processing (QIP)is an exciting new field showing a lot of promise as a powerful addition to the arsenal of Image Processing techniques. Representing image pixel by pixel using classical information requires an enormous amount of computational resources. Hence, exploring methods to represent images in a different paradigm of information is important. In this work, we study the representation of images in Quantum Information. The main motivation for this pursuit is the ability of storing N bits of classical information in only log(2N) quantum bits (qubits). The promising first step was the exponentially efficient implementation of the Fourier transform in quantum computers as compared to Fast Fourier Transform in classical computers. In addition, images encoded in quantum information could obey unique quantum properties like superposition or entanglement.
Quantum computing is a rapidly developing field with faster computational capabilities than classical computing.The popularity of quantum computing has reached the field of image processing, particularly with a breakthrough method known as Quantum Hadamard Edge Detection.This approach represents a significant advancement in edge detection techniques using quantum computing.Quantum Hadamard Edge Detection is a method that can detect image edges more quickly than classical methods with exponential acceleration.This paper explains the Quantum Hadamard Edge Detection method in detail, including how it is implemented, a time complexity explanation, some experiments, and future research directions.Our experiments utilize a quantum computer simulator and employ four measurement metrics: Structural Similarity Index, Figure of Merit, Entropy, and a Proposed Metric with radius-based features, to detect simple binary images, MNIST images, and the Berkeley Segmentation datasets.We recognize the potential of quantum computing and believe that image processing with quantum representation will make processing more efficient and significantly valuable in the future.