Induced on-demand revival in coined quantum walks on infinite $d$-dimensional lattices
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866909198330101760 |
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| author | Jayakody, Mahesh N. Paiva, Ismael L. Nanayakkara, Asiri Cohen, Eliahu |
| author_facet | Jayakody, Mahesh N. Paiva, Ismael L. Nanayakkara, Asiri Cohen, Eliahu |
| contents | The study of recurrences and revivals in quantum systems has attracted a great deal of interest because of its importance in the control of quantum systems and its potential use in developing new technologies. In this work, we introduce a protocol to induce full-state revivals in a huge class of quantum walks on a $d$-dimensional lattice governed by a $c$-dimensional coin system. The protocol requires two repeated interventions in the coin degree of freedom. We also present a characterization of the walks that admits such a protocol. Moreover, we modify the quantity known as Pólya number, typically used in the study of recurrences in classical random walks and quantum walks, to create a witness of the first revival of the walk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_03307 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Induced on-demand revival in coined quantum walks on infinite $d$-dimensional lattices Jayakody, Mahesh N. Paiva, Ismael L. Nanayakkara, Asiri Cohen, Eliahu Quantum Physics The study of recurrences and revivals in quantum systems has attracted a great deal of interest because of its importance in the control of quantum systems and its potential use in developing new technologies. In this work, we introduce a protocol to induce full-state revivals in a huge class of quantum walks on a $d$-dimensional lattice governed by a $c$-dimensional coin system. The protocol requires two repeated interventions in the coin degree of freedom. We also present a characterization of the walks that admits such a protocol. Moreover, we modify the quantity known as Pólya number, typically used in the study of recurrences in classical random walks and quantum walks, to create a witness of the first revival of the walk. |
| title | Induced on-demand revival in coined quantum walks on infinite $d$-dimensional lattices |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2201.03307 |