Quantum Search Algorithm With More Reliable Behaviour Using Partial Diffusion

Abstract

In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system (\{\it Partial Diffusion Operator\}) to propose a quantum search algorithm runs in $O(\sqrt{N}/M\})$ for searching unstructured list of size $N$ with $M$ matches such that, $1\le M\le N$. We will show that the performance of the algorithm is more reliable than known quantum search algorithms especially for multiple matches within the search space. A performance comparison with Grover's algorithm will be provided.