An information geometric viewpoint of algorithms in quantum computing

We show that quantum information geometry can be used to characterize Grover's searching algorithm. Specifically, quantifying the notion of quantum distinguishability between parametric density operators by means of the Wigner-Yanase quantum information metric, we uncover 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 continuos approximation of the parametric quantum out-put state in Grover's algorithm.