Grover Search as a Naturally Occurring Phenomenon - Laboratoire Méthodes Formelles Accéder directement au contenu
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2020

Grover Search as a Naturally Occurring Phenomenon

Résumé

We provide first evidence that under certain conditions, 1/2-spin fermions may naturally behave like a Grover search, looking for topological defects in a material. The theoretical framework is that of discrete-time quantum walks (QWs), i.e., local unitary matrices that drive the evolution of a single particle on the lattice. Some QWs are well known to recover the (2+1)–dimensional Dirac equation in continuum limit, i.e., the free propagation of the 1/2-spin fermion. We study two such Dirac QWs, one on the square grid and the other on a triangular grid reminiscent of graphenelike materials. The numerical simulations show that the walker localizes around the defects in O(N) steps with probability O(1/logN), in line with previous QW search on the grid. The main advantage brought by those of this Letter is that they could be implemented as “naturally occurring” freely propagating particles over a surface featuring topological defects—without the need for a specific oracle step. From a quantum computing perspective, however, this hints at novel applications of QW search: instead of using them to look for “good” solutions within the configuration space of a problem, we could use them to look for topological properties of the entire configuration space.
Fichier principal
Vignette du fichier
1908.11213.pdf (1.01 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03594726 , version 1 (04-09-2023)
hal-03594726 , version 2 (23-11-2023)

Identifiants

Citer

Mathieu Roget, Stéphane Guillet, Pablo Arrighi, Giuseppe Di Molfetta. Grover Search as a Naturally Occurring Phenomenon. 2023. ⟨hal-03594726v1⟩
150 Consultations
40 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More