A Comment on Fisher Information and Quantum Algorithms

Details A Comment on Fisher Information and Quantum Algorithms A Comment on Fisher Information and Quantum Algorithms

1999-10-27

arxiv.org/abs/quant-ph/9910115v3

Physics

Quantum Physics

5 pages, LaTex file, Shor's factoring algorithm discussion added (new sections 5 and 6)

Scientific paper

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.

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