Geometric transformations of multidimensional color images based on NASS

TL;DR

This paper introduces quantum algorithms for geometric transformations of multidimensional color images using NASS, enabling efficient implementation with polynomial gate complexity for various transformations.

Contribution

It presents novel quantum algorithms for geometric image transformations based on NASS, with efficient circuit constructions and complexity analysis.

Findings

Transformations implemented with O(n) gates

Quantum circuits use polynomial numbers of gates

Facilitates low-complexity quantum image applications

Abstract

We present quantum algorithms to realize geometric transformations (two-point swappings, symmetric flips, local flips, orthogonal rotations, and translations) based on an $n$-qubit normal arbitrary superposition state (NASS). These transformations are implemented using quantum circuits consisting of basic quantum gates, which are constructed with polynomial numbers of single-qubit and two-qubit gates. Complexity analysis shows that the global operators (symmetric flips, local flips, orthogonal rotations) can be implemented with $O(n)$ gates. The proposed geometric transformations are used to facilitate applications of quantum images with low complexity.