基于NASS的多维彩色图像几何变换
Geometric transformations of multidimensional color images based on NASS
摘要：
我们提出了基于$n$ -量子比特正常任意叠加态（NASS）实现几何变换（两点交换、对称翻转、局部翻转、正交旋转和平移）的量子算法。这些转换是使用由基本量子门组成的量子线路来实现的，基本量子门由多项式数量的单量子比特和双量子比特门构成。复杂性分析表明，全局操作（对称翻转，局部翻转，正交旋转）可以实现与$O(n)$门。所提出的几何变换用于促进低复杂度的量子图像的应用。
英文摘要：
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.
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