Generalized exceptional quantum walk search
We mainly study exceptional configuration for coined quantum walk search. For searching on a two-dimensional grid by AKR algorithm, we find some new classes of exceptional configurations that cannot be found by the AKR algorithm effectively and the known diagonal configuration can be regarded as its...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/abca5d |
| _version_ | 1827872953979633664 |
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| author | Meng Li Yun Shang |
| author_facet | Meng Li Yun Shang |
| author_sort | Meng Li |
| collection | DOAJ |
| description | We mainly study exceptional configuration for coined quantum walk search. For searching on a two-dimensional grid by AKR algorithm, we find some new classes of exceptional configurations that cannot be found by the AKR algorithm effectively and the known diagonal configuration can be regarded as its special case. Meanwhile, we give two modified quantum walk models that can improve the success probability in the exceptional configurations by numerical simulation. Furthermore, we introduce the concept of generalized exceptional configuration and consider search by quantum walk on a cycle with Grover coin. We find that the most common coin combination model ( G , −), where G is a Grover diffusion transformation, is a generalized exceptional configuration when just searching one marked vertex on the cycle. In the end, we find generalized exceptional configuration has a different evolution of quantum coherence from exceptional configuration. These extend largely the range of exceptional configuration of quantum walk search in some sense. |
| first_indexed | 2024-03-12T16:30:43Z |
| format | Article |
| id | doaj.art-9ffe1061eca8412dbf7261e8841f4338 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:30:43Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-9ffe1061eca8412dbf7261e8841f43382023-08-08T15:30:05ZengIOP PublishingNew Journal of Physics1367-26302020-01-01221212303010.1088/1367-2630/abca5dGeneralized exceptional quantum walk searchMeng Li0Yun Shang1https://orcid.org/0000-0003-1466-5970Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences , Beijing 100190, People’s Republic of China; School of Mathematical Sciences, University of Chinese Academy of Sciences , Beijing 100049, People’s Republic of ChinaInstitute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences , Beijing 100190, People’s Republic of China; NCMIS, MDIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences , Beijing, 100190, People’s Republic of ChinaWe mainly study exceptional configuration for coined quantum walk search. For searching on a two-dimensional grid by AKR algorithm, we find some new classes of exceptional configurations that cannot be found by the AKR algorithm effectively and the known diagonal configuration can be regarded as its special case. Meanwhile, we give two modified quantum walk models that can improve the success probability in the exceptional configurations by numerical simulation. Furthermore, we introduce the concept of generalized exceptional configuration and consider search by quantum walk on a cycle with Grover coin. We find that the most common coin combination model ( G , −), where G is a Grover diffusion transformation, is a generalized exceptional configuration when just searching one marked vertex on the cycle. In the end, we find generalized exceptional configuration has a different evolution of quantum coherence from exceptional configuration. These extend largely the range of exceptional configuration of quantum walk search in some sense.https://doi.org/10.1088/1367-2630/abca5dgeneralized exceptional configurationexceptional configurationcoined quantum walkquantum walk search |
| spellingShingle | Meng Li Yun Shang Generalized exceptional quantum walk search New Journal of Physics generalized exceptional configuration exceptional configuration coined quantum walk quantum walk search |
| title | Generalized exceptional quantum walk search |
| title_full | Generalized exceptional quantum walk search |
| title_fullStr | Generalized exceptional quantum walk search |
| title_full_unstemmed | Generalized exceptional quantum walk search |
| title_short | Generalized exceptional quantum walk search |
| title_sort | generalized exceptional quantum walk search |
| topic | generalized exceptional configuration exceptional configuration coined quantum walk quantum walk search |
| url | https://doi.org/10.1088/1367-2630/abca5d |
| work_keys_str_mv | AT mengli generalizedexceptionalquantumwalksearch AT yunshang generalizedexceptionalquantumwalksearch |