Classical color image processing, image recognition, and machine learning introduce nonlinearity, causing the collapse of the quantum state into classical probability perceptrons after measurements, due to the inherent linearity of quantum computing. To address this challenge, quaternion-based arithmetic offers a promising approach. By treating the primary color components as a single unit using quaternion algebra, nonlinear relationships can be implemented, effectively manipulating higher-dimensional color data. This article aims to achieve efficient and accurate color quantum image processing (QIP) by introducing new quaternion quantum-based color imaging tools based on multiplicative arithmetic on two-qubits and quantum superpositions. The approach includes the concept of a quaternion Fourier transform (QFT) in two-qubit-based color image representation. To end, we discuss possible applications of the proposed methods in color quantum imaging.

中文翻译：

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量子信息处理中基于四元数的算法：一种有前途的高效彩色量子成像方法[超复杂信号和图像处理]


由于量子计算固有的线性性，经典的彩色图像处理、图像识别和机器学习引入了非线性，导致测量后量子态崩溃为经典概率感知器。为了应对这一挑战，基于四元数的算术提供了一种有前途的方法。通过使用四元数代数将原色分量视为单个单元，可以实现非线性关系，从而有效地操纵更高维的颜色数据。本文旨在通过引入基于两个量子位乘法运算和量子叠加的新型四元数量子彩色成像工具，实现高效、准确的彩色量子图像处理（QIP）。该方法包括基于两个量子位的彩色图像表示中的四元数傅里叶变换（QFT）的概念。最后，我们讨论了所提出的方法在彩色量子成像中的可能应用。