A Comment on Fisher Information and Quantum Algorithms

摘要

We show that Grover's algorithm defines a geodesic in quantum Hilbert spacewith the Fubini-Study metric. From statistical point of view Grover's algorithmis characterized by constant Fisher's function. Quantum algorithms changingcomplexity class as Shor's factorization does not preserve constant Fisher'sinformation. An adiabatic quantum factorization algorithm in non polynomialtime is presented to exemplify the result.