Quantum Search Algorithm with more Reliable Behaviour using Partial Diffusion

In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system (Partial Diffusion Operator) to propose a quantum search algorithm runs in O( √ N/M ) for searching unstructured list of size N with M matches such that, 1 ≤ M ≤ 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.