Enhanced quantum searching via entanglement and partial diffusion

In this paper, we will define a quantum operator that performs the standard inversion about the mean only on a subspace of the system (Partial Diffusion Operator  ). This operator is used together with entanglement in a quantum search algorithm that runs in O(N/M) for searching an unstructured list of size NN with MM matches such that 1≤M≤N1≤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 MM is unknown in advance in O(N/M) such that 1≤M≤N1≤M≤N.