A Comment on Fisher Information and Quantum Algorithms

Abstract

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)

References in corpus (2)

• Quantum Mechanics helps in searching for a needle in a haystack
• Grover's quantum searching algorithm is optimal

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