Quantum Searching via Entanglement and Partial Diffusion

In this paper, we will define a quantum operator that performs the inversion about the mean only on a subspace of the system (Partial Diffusion Operator). This operator is used in a quantum search algorithm that runs in O( √ N/M) for searching an 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 fixed operators quantum search algorithms especially for multiple matches where we can get a solution after a single iteration with probability over 90% if the number of matches is approximately more than one-third of the search space. We will show that the algorithm will be able to handle the case where the number of matches M is unknown in advance such that 1 ≤ M ≤ N in O( √ N/M). A performance comparison with Grover’s algorithm will be provided.