Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutions
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numeric...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/16/2/023002 |
| _version_ | 1797751499880660992 |
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| author | B Kollár J Novotný T Kiss I Jex |
| author_facet | B Kollár J Novotný T Kiss I Jex |
| author_sort | B Kollár |
| collection | DOAJ |
| description | Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numerical methods. We develop novel analytic methods based on the theory of random unitary operations which help us to determine explicitly the asymptotic dynamics of quantum walks on two-dimensional finite integer lattices with percolation. Based on this theory, we find new unexpected features of percolated walks like asymptotic position inhomogeneity or special directional symmetry breaking. |
| first_indexed | 2024-03-12T16:50:28Z |
| format | Article |
| id | doaj.art-47daa7d69bb84e3aa4eb29308c3dadaa |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:50:28Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-47daa7d69bb84e3aa4eb29308c3dadaa2023-08-08T11:21:53ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116202300210.1088/1367-2630/16/2/023002Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutionsB Kollár0J Novotný1T Kiss2I Jex3Wigner RCP, SZFKI, Konkoly-Thege Miklós út 29-33, H-1121 Budapest, Hungary; Institute of Physics, University of Pécs , Ifjúság útja 6, H-7624 Pécs, HungaryDepartment of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague , Břehová 7, 115 19 Praha 1—Staré Město, Czech RepublicWigner RCP, SZFKI, Konkoly-Thege Miklós út 29-33, H-1121 Budapest, HungaryDepartment of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague , Břehová 7, 115 19 Praha 1—Staré Město, Czech RepublicQuantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numerical methods. We develop novel analytic methods based on the theory of random unitary operations which help us to determine explicitly the asymptotic dynamics of quantum walks on two-dimensional finite integer lattices with percolation. Based on this theory, we find new unexpected features of percolated walks like asymptotic position inhomogeneity or special directional symmetry breaking.https://doi.org/10.1088/1367-2630/16/2/023002 |
| spellingShingle | B Kollár J Novotný T Kiss I Jex Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutions New Journal of Physics |
| title | Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutions |
| title_full | Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutions |
| title_fullStr | Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutions |
| title_full_unstemmed | Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutions |
| title_short | Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutions |
| title_sort | percolation induced effects in two dimensional coined quantum walks analytic asymptotic solutions |
| url | https://doi.org/10.1088/1367-2630/16/2/023002 |
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