Mixed Grover: A Hybrid Version to Improve Grover's Algorithm for Unstructured Database Search

In this article, we propose a new strategy to exploit Grover's algorithm for unstructured search problems. We first show that running Grover's routine with a reduced number of iterations but allowing several trials presents a complexity advantage while keeping the same success probability. Then, by a theoretical analysis of the performance, we provide a generic procedure to parameterize the number of iterations $k$ within one shot of Grover's algorithm and the maximum number of trials $T$, given a targeted success $p$ and the size of the database $N$. At the end, we highlight that this new approach permits to reduce the computational time by at least 10% for $p \geq 0.999$ independently of the size of the database.