Grover search revisited: Application to image pattern matching

The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various type of quantum algorithms, with guaranteed speedup query complexity. However, there have been no proposal to realize the original motivating application algorithm, i.e., database search or more broadly pattern matching a practical setting, mainly due technical difficulty efficiently implementing data loading and processes. In this paper, we propose that approximately executes entire algorithm. key idea is use recently proposed approximate encoding method on shallow circuit, together easily implementable inversion-test operation realizing projected state having similarity data, followed by independent target index. We provide thorough demonstration problem image matching.