On Grover’s search algorithm from a quantum information geometry viewpoint

We present an information geometric characterization of Grover’s quantum search algorithm. First, we quantify the notion of quantum distinguishability between parametric density operators by means of the Wigner–Yanase quantum information metric. We then show that the quantum searching problem can be recast in an information geometric framework where Grover’s dynamics is characterized by a geodesic on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover’s algorithm. We also discuss possible deviations from Grover’s algorithm within this quantum information geometric setting.