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...

We analyze the responses of a quantum search algorithm to an external monochromatic field and to the decoherences introduced through measurement processes. The external field in general affects the functioning of the search algorithm. However, depending on the values of the field parameters,...

We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to N, where N is the database size. This search algorithm can be implemented using any Hamiltonian with a discrete energy spectrum through...

The article continues a presentation of modern quantum mathematics backgrounds started in [Quantum Mathematics and its Applications. Part 1. Automatyka, vol. 6, AGH Publisher, Krakow, 2002, No. 1, pp. 234–2412; Quantum Mathematics: Holonomic Computing Algorithms and Their Applications. Part 2....