Quantum Image Matching

TL;DR

This paper presents a quantum image matching algorithm that focuses on a single pixel, addressing measurement limitations in quantum image processing, and demonstrates its efficiency compared to classical methods.

Contribution

It introduces a quantum image matching scheme that targets one pixel and accounts for measurement constraints, improving efficiency over classical approaches.

Findings

The quantum scheme achieves complexity $O(2^{n})$, significantly better than classical $O(2^{2n+2m})$.

The algorithm uses Grover's algorithm to increase the probability of measuring the target pixel.

Measurement is performed only once, reducing the number of required executions.

Abstract

Quantum image processing (QIP) means the quantum based methods to speed up image processing algorithms. Many quantum image processing schemes claim that their efficiency are theoretically higher than their corresponding classical schemes. However, most of them do not consider the problem of measurement. As we all know, measurement will lead to collapse. That is to say, executing the algorithm once, users can only measure the final state one time. Therefore, if users want to regain the results (the processed images), they must execute the algorithms many times and then measure the final state many times to get all the pixels' values. If the measurement process is taken into account, whether or not the algorithms are really efficient needs to be reconsidered. In this paper, we try to solve the problem of measurement and give a quantum image matching algorithm. Unlike most of the QIP algorithms, our scheme interests only one pixel (the target pixel) instead of the whole image. It modifies the probability of pixels based on Grover's algorithm to make the target pixel to be measured with higher probability, and the measurement step is executed only once. An example is given to explain the algorithm more vividly. Complexity analysis indicates that the quantum scheme's complexity is $O(2^{n})$ in contradistinction to the classical scheme's complexity $O(2^{2n+2m})$, where $m$ and $n$ are integers related to the size of images.