Quantum algorithm for optical-template recognition with noise filtering

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 requires just a few incident photons and is thus suitable for very sensitive pictures (similar to the Elitzur-Vaidman problem). Furthermore, for a 2ⁿ×2ᵐ image, $O(n+m)$ 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 512×512 pixels, we have numerically simulated the unitary operations in order to demonstrate the applicability of the algorithm and to analyze its fault tolerance.