论文标题
用于数字图像处理的混合古典量子算法
A hybrid classical-quantum algorithm for digital image processing
论文作者
论文摘要
提出了一种用于评估多维Walsh-Hadamard变换及其在量子图像处理中的应用的混合经典方法。在这种方法中，使用量子Hadamard大门（以及状态准备，迁移，缩放和测量操作）获得了多维Walsh-Hadamard变换。 The proposed approach for evaluation of multidimensional Walsh-Hadamard transform has a considerably lower computational complexity (involving $O(N^d)$ operations) in contrast to classical Fast Walsh-Hadamard transform (involving $O(N^d~\log_2 N^d)$ operations), where $d$ and $N$ denote the number of dimensions and degrees of freedom along each dimension.与许多其他量子图像表示和量子图像处理框架不同，我们提出的方法有效地利用了Qubits，其中只有$ \ log_2 n $ Qubits足以顺序处理$ n \ times n $像素的图像。通过与基本图像滤波和定期频段降噪相关的计算示例，证明了所提出的方法的选定应用（对于$ d = 2 $），发现结果令人满意。
A hybrid classical-quantum approach for evaluation of multi-dimensional Walsh-Hadamard transforms and its applications to quantum image processing are proposed. In this approach, multidimensional Walsh-Hadamard transforms are obtained using quantum Hadamard gates (along with state-preparation, shifting, scaling and measurement operations). The proposed approach for evaluation of multidimensional Walsh-Hadamard transform has a considerably lower computational complexity (involving $O(N^d)$ operations) in contrast to classical Fast Walsh-Hadamard transform (involving $O(N^d~\log_2 N^d)$ operations), where $d$ and $N$ denote the number of dimensions and degrees of freedom along each dimension. Unlike many other quantum image representation and quantum image processing frameworks, our proposed approach makes efficient use of qubits, where only $\log_2 N $ qubits are sufficient for sequential processing of an image of $ N \times N $ pixels. Selected applications of the proposed approach (for $ d=2 $) are demonstrated via computational examples relevant to basic image filtering and periodic banding noise removal and the results were found to be satisfactory.
