A Comment on Fisher Information and Quantum Algorithms
Abstract
Description
We show that Grover's algorithm defines a geodesic in quantum Hilbert space with the Fubini-Study metric. From statistical point of view Grover's algorithm is characterized by constant Fisher's function. Quantum algorithms changing complexity class as Shor's factorization does not preserve constant Fisher's information. An adiabatic quantum factorization algorithm in non polynomial time is presented to exemplify the result.
5 pages, LaTex file, Shor's factoring algorithm discussion added (new sections 5 and 6)
5 pages, LaTex file, Shor's factoring algorithm discussion added (new sections 5 and 6)