Quantum walks and quantum search on graphene lattices
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 o...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Published: |
American Physical Society
2015
|
| Online Access: | https://eprints.nottingham.ac.uk/46594/ |
| _version_ | 1848797362797936640 |
|---|---|
| author | Foulger, Iain Gnutzmann, Sven Tanner, Gregor |
| author_facet | Foulger, Iain Gnutzmann, Sven Tanner, Gregor |
| author_sort | Foulger, Iain |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:02:41Z |
| format | Article |
| id | nottingham-46594 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:02:41Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-465942020-05-04T17:10:33Z https://eprints.nottingham.ac.uk/46594/ Quantum walks and quantum search on graphene lattices Foulger, Iain Gnutzmann, Sven Tanner, Gregor 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. American Physical Society 2015-06-18 Article PeerReviewed Foulger, Iain, Gnutzmann, Sven and Tanner, Gregor (2015) Quantum walks and quantum search on graphene lattices. Physical Review A, 91 (6). 062323/1-062323/15. ISSN 2469-9934 https://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.062323 doi:10.1103/PhysRevA.91.062323 doi:10.1103/PhysRevA.91.062323 |
| spellingShingle | Foulger, Iain Gnutzmann, Sven Tanner, Gregor Quantum walks and quantum search on graphene lattices |
| title | Quantum walks and quantum search on graphene lattices |
| title_full | Quantum walks and quantum search on graphene lattices |
| title_fullStr | Quantum walks and quantum search on graphene lattices |
| title_full_unstemmed | Quantum walks and quantum search on graphene lattices |
| title_short | Quantum walks and quantum search on graphene lattices |
| title_sort | quantum walks and quantum search on graphene lattices |
| url | https://eprints.nottingham.ac.uk/46594/ https://eprints.nottingham.ac.uk/46594/ https://eprints.nottingham.ac.uk/46594/ |