Controlled transport in chiral quantum walks on graphs
We investigate novel transport properties of chiral continuous-time quantum walks (CTQWs) on graphs. By employing a gauge transformation, we demonstrate that CTQWs on chiral chains are equivalent to those on non-chiral chains, but with additional momenta from initial wave packets. This explains the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/acec90 |
| _version_ | 1797739512354308096 |
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| author | Yi-Cong Yu Xiaoming Cai |
| author_facet | Yi-Cong Yu Xiaoming Cai |
| author_sort | Yi-Cong Yu |
| collection | DOAJ |
| description | We investigate novel transport properties of chiral continuous-time quantum walks (CTQWs) on graphs. By employing a gauge transformation, we demonstrate that CTQWs on chiral chains are equivalent to those on non-chiral chains, but with additional momenta from initial wave packets. This explains the novel transport phenomenon numerically studied in (Khalique et al 2021 New J. Phys. 23 083005). Building on this, we delve deeper into the analysis of chiral CTQWs on the Y-junction graph, introducing phases to account for the chirality. The phase plays a key role in controlling both asymmetric transport and directed complete transport among the chains in the Y-junction graph. We systematically analyze these features through a comprehensive examination of the chiral CTQW on a Y-junction graph. Our analysis shows that the CTQW on Y-junction graph can be modeled as a combination of three wave functions, each of which evolves independently on three effective open chains. By constructing a lattice scattering theory, we calculate the phase shift of a wave packet after it interacts with the potential-shifted boundary. Our results demonstrate that the interplay of these phase shifts leads to the observed enhancement and suppression of quantum transport. The explicit condition for directed complete transport or $100\%$ efficiency is analytically derived. Our theory has applications in building quantum versions of binary tree search algorithms. |
| first_indexed | 2024-03-12T13:59:11Z |
| format | Article |
| id | doaj.art-d9219410b6e04c7fad169173db9fdf08 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T13:59:11Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-d9219410b6e04c7fad169173db9fdf082023-08-22T11:02:34ZengIOP PublishingNew Journal of Physics1367-26302023-01-0125808303410.1088/1367-2630/acec90Controlled transport in chiral quantum walks on graphsYi-Cong Yu0https://orcid.org/0000-0003-1721-7532Xiaoming Cai1https://orcid.org/0000-0002-3646-8196Wuhan Institute of Physics and Mathematics ,Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences , Wuhan, Hubei, People’s Republic of ChinaWuhan Institute of Physics and Mathematics ,Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences , Wuhan, Hubei, People’s Republic of ChinaWe investigate novel transport properties of chiral continuous-time quantum walks (CTQWs) on graphs. By employing a gauge transformation, we demonstrate that CTQWs on chiral chains are equivalent to those on non-chiral chains, but with additional momenta from initial wave packets. This explains the novel transport phenomenon numerically studied in (Khalique et al 2021 New J. Phys. 23 083005). Building on this, we delve deeper into the analysis of chiral CTQWs on the Y-junction graph, introducing phases to account for the chirality. The phase plays a key role in controlling both asymmetric transport and directed complete transport among the chains in the Y-junction graph. We systematically analyze these features through a comprehensive examination of the chiral CTQW on a Y-junction graph. Our analysis shows that the CTQW on Y-junction graph can be modeled as a combination of three wave functions, each of which evolves independently on three effective open chains. By constructing a lattice scattering theory, we calculate the phase shift of a wave packet after it interacts with the potential-shifted boundary. Our results demonstrate that the interplay of these phase shifts leads to the observed enhancement and suppression of quantum transport. The explicit condition for directed complete transport or $100\%$ efficiency is analytically derived. Our theory has applications in building quantum versions of binary tree search algorithms.https://doi.org/10.1088/1367-2630/acec90chiral quantum walkdirected quantum transportY-junction graphscattering on lattice |
| spellingShingle | Yi-Cong Yu Xiaoming Cai Controlled transport in chiral quantum walks on graphs New Journal of Physics chiral quantum walk directed quantum transport Y-junction graph scattering on lattice |
| title | Controlled transport in chiral quantum walks on graphs |
| title_full | Controlled transport in chiral quantum walks on graphs |
| title_fullStr | Controlled transport in chiral quantum walks on graphs |
| title_full_unstemmed | Controlled transport in chiral quantum walks on graphs |
| title_short | Controlled transport in chiral quantum walks on graphs |
| title_sort | controlled transport in chiral quantum walks on graphs |
| topic | chiral quantum walk directed quantum transport Y-junction graph scattering on lattice |
| url | https://doi.org/10.1088/1367-2630/acec90 |
| work_keys_str_mv | AT yicongyu controlledtransportinchiralquantumwalksongraphs AT xiaomingcai controlledtransportinchiralquantumwalksongraphs |