Identification of Desired Pixels in an Image Using Grover's Quantum Search Algorithm

TL;DR

This paper explores using Grover's quantum search algorithm to identify darker pixels in a small grayscale image, demonstrating quantum image processing applications and comparing classical and quantum approaches.

Contribution

It presents a novel application of Grover's algorithm to quantum image processing by locating darker pixels in a 2x2 grayscale image, including implementation methods.

Findings

Grover's algorithm successfully identifies darker pixels in quantum image processing.

Quantum approach shows quadratic speed-up over classical methods.

Implementation on simulated quantum images demonstrates feasibility.

Abstract

Quantum Information Theory promises to speed up computation so is observed in real quantum computers as proved to its classical counterpart. This revolutionizes every field linked directly or indirectly with computation. Grover algorithm in quantum information gives quadratic speed up in unstructured database search. With the availability of public online resources for quantum computers like IBM, quantum image processing came into the picture for making use of quantum computers in the image processing field. Our research interest is to find all darker pixels in a 2x2 grayscale image using Grover's algorithm. We studied it in two different ways. In the first method, I ran Grover's algorithm on the python generated classical image. In the second method, I converted a python-generated 2x2 image into a quantum image and then ran Grover's algorithm to locate the darker pixels. As has been observed in complexity analysis, Grover's unstructured search has the O(2^{n}) while as for classical schemes O(2^{2n+2m}), where m and n denote the dimensions of the image.