Grover search revisited; application to image pattern matching

TL;DR

This paper proposes a practical quantum algorithm for database search and image pattern matching using approximate amplitude encoding and shallow circuits, enabling more feasible implementation of Grover's algorithm.

Contribution

It introduces a new quantum algorithm that approximately implements Grover's search with shallow circuits and demonstrates its application to image pattern matching.

Findings

Algorithm effectively performs pattern matching on images.

Uses approximate amplitude encoding with shallow quantum circuits.

Demonstrates practical feasibility of Grover-based search in image processing.

Abstract

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