Description of the Grover algorithm based on geometric considerations - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Description of the Grover algorithm based on geometric considerations

Résumé

This paper concerns the Grover algorithm that permits to make amplification of quantum states previously tagged by an Oracle. Grover's algorithm allows searches in an unstructure database of n entries finding a marked element with a quadratic speedup. The algorithm requires a predefined number of runs to succeed with probability close to one.This article provides a description of the amplitude amplification quantum algorithm mechanism in a very short computational way, based on tensor products and provides a geometric presentation of the successive system states. All the basis changes are fully described to provide an alternative to the wide spread Grover description based only on matrices and complex tensor computation. Our experiments encompass numerical evaluations of circuit using the Qiskit library of IBM that meet the theoretical considerations

Dates et versions

hal-03839168 , version 1 (04-11-2022)

Identifiants

Citer

Gérard Fleury, Philippe Lacomme. Description of the Grover algorithm based on geometric considerations. 2022. ⟨hal-03839168⟩
23 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More