A Long-algorithm Based Variational Quantum Scheme for Pattern Matching Problem

Grover algorithm is a popular model in quantum computation field and has the advantage of outperforming its classical counterpart in terms of searching speed, hence it has been applied in various domains such as pattern matching. Unfortunately, there are two central issue for this quantum search algorithm, i.e., Grover algorithm, in practical application that firstly it can only achieve a probability nearing 100% rather than exactly, secondly it tends to require a deep quantum circuit. In this work, we propose a Long-algorithm based quantum scheme for pattern matching problem, which can effectively enhance the success probability of quantum pattern matching and mitigate the needs for quantum computing resources. The performance of this scheme is demonstrated numerically, validating our design.