带噪声滤波的光学模板识别量子算法
Quantum algorithm for optical template recognition with noise filtering
摘要：
我们提出了一个概率量子算法，决定是否单色图片匹配给定的模板（或一组模板）。作为经典模式识别的一个主要优点，该算法只需要几个入射光子，因此适用于非常敏感的图像（类似于Elitzur-Vaidman问题）。此外，对于$2^{n}\times 2^{m}$图像，$\ord(n+m)$量子位是足够的。利用量子傅里叶变换，可以通过滤除图像中的小尺度噪声来提高量子算法的容错性。以具有$512\times512$像素的图像为例，我们对酉运算进行了数值模拟，以证明该算法的适用性并分析其容错性。
英文摘要：
We propose a probabilistic quantum algorithm that decides whether a monochrome picture matches a given template (or one out of a set of templates). As a major advantage to classical pattern recognition, the algorithm just requires a few incident photons and is thus suitable for very sensitive pictures (similar to the Elitzur-Vaidman problem). Furthermore, for a $2^{n}\times 2^{m}$ image, $\ord(n+m)$ qubits are sufficient. Using the quantum Fourier transform, it is possible to improve the fault tolerance of the quantum algorithm by filtering out small-scale noise in the picture. For example images with $512\times512$ pixels, we have numerically simulated the unitary operations in order to demonstrate the applicability of the algorithm and to analyze its fault tolerance.
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