Additive composition formulation of the iterative Grover algorithm

In the Grover-type quantum search process a search operator is iteratively applied, say, k times, on the initial uniform superposition database state. We present an additive decomposition scheme such that the iteration process is expressed, in the computational space, as a linear combination of k operators, each of which consists of a single Grover-search followed by an overall phase-rotation. The value of k and the rotation phase are the same …