A Generalization of Grover's Algorithm
Year: 2000
Type: preprint
Abstract: We investigate the necessary and sufficient conditions in order that a unitary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expence of the other components. This leads to a general method which allows, given a vector and one of its components we want to amplify, to choose the optimal unitary operator which realizes that goal. Grover’s quantum algorithm is shown to be a particular case of our general method. However the general structure of the unitary we find is remarkably similar to that of Grover’s one: a sign flip of one component combined with a reflection with respect to a vector. In Grover’s case this vector is fixed; in our case it depends on a parameter and this allows optimization. 1 Unitary operators which increase the probability of the |0> component of a pre-assigned vector
Authors: Luigi Accardi, Ruben Sabbadini
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2964056985