Quantum walks and quantum search on graphene lattices

Foulger, Iain; Gnutzmann, Sven; Tanner, Gregor

Abstract

Quantum walks have been very useful in developing search algorithms in quantum information, in particular for devising of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in two-dimensional lattices has proved difficult, requiring additional degrees of freedom. Here, we demonstrate that a continuous-time quantum walk search is possible in two dimensions by changing the search topology to a graphene lattice, utilizing the Dirac point in the energy spectrum. This is made possible by making a change to standard methods of marking a particular site in the lattice. Various ways of marking a site are shown to result in successful search protocols. We further establish that the search can be adapted to transfer probability amplitude across the lattice between specific lattice sites thus establishing a line of communication between these sites.

Citation

Foulger, I., Gnutzmann, S., & Tanner, G. (2015). Quantum walks and quantum search on graphene lattices. Physical Review A, 91(6), Article 062323. https://doi.org/10.1103/PhysRevA.91.062323

• Journal Article Type: Article
• Acceptance Date: Jan 28, 2015
• Publication Date: Jun 18, 2015
• Deposit Date: Sep 25, 2017
• Publicly Available Date: Sep 25, 2017
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 91
• Issue: 6
• Article Number: 062323
• DOI: https://doi.org/10.1103/PhysRevA.91.062323
• Public URL: https://nottingham-repository.worktribe.com/output/754156
• Publisher URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.062323
• Additional Information: ©2015 American Physical Society
• Contract Date: Sep 25, 2017