Optimal fault-tolerant quantum comparators for image binarization

Quantum image processing focuses on the use of quantum computing in the field of digital image processing. In the last few years, this technique has emerged since the properties inherent to quantum mechanics would provide the computing power required to solve hard problems much faster than classical computers. Binarization is often recognized to be one of the most important steps in image processing systems. Image binarization consists of converting the digital image into a black and white image, so that the essential properties of the image are preserved. In this paper, we propose a quantum circuit for image binarization based on two novel comparators. These comparators are focused on optimizing the number of T gates needed to build them. The use of T gates is essential for quantum circuits to counteract the effects of internal and external noise. However, these gates are highly expensive, and its slowness also represents a common bottleneck in this type of circuit. The proposed quantum comparators have been compared with other state-of-the-arts comparators. The analysis of the implementations has shown our comparators are the best option when noise is a problem and its reduction is mandatory.