2000/12/27 by Luigi Accardi, Accardi, Luigi, Ruben Sabbadini +1
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0012143
20 pages, no figures
arxiv created 2000/12/27 · openalex publication_date 2000/12/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 expense 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.