Clifford Algebras, Spin Groups and Qubit Trees
Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of superfluous branches. The usual Jordan–Wigner construction...
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Quanta
2022-12-01
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| Series: | Quanta |
| Online Access: | https://dankogeorgiev.com/ojs/index.php/quanta/article/view/72 |
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| author | Alexander Yurievich Vlasov |
| author_facet | Alexander Yurievich Vlasov |
| author_sort | Alexander Yurievich Vlasov |
| collection | DOAJ |
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Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of superfluous branches. The usual Jordan–Wigner construction also may be formally obtained in this approach by bringing the process up to trivial qubit chain (trunk). The methods can also be used for effective simulation of some quantum circuits corresponding to the binary tree structure. The modeling of more general qubit trees, as well as the relationship with the mapping used in the Bravyi–Kitaev transformation, are also briefly discussed.
Quanta 2022; 11: 97–114.
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| format | Article |
| id | doaj-art-e314043e496a4e8a8c058b2a1f2b78ab |
| institution | Kabale University |
| issn | 1314-7374 |
| language | English |
| publishDate | 2022-12-01 |
| publisher | Quanta |
| record_format | Article |
| series | Quanta |
| spelling | doaj-art-e314043e496a4e8a8c058b2a1f2b78ab2025-08-20T03:47:17ZengQuantaQuanta1314-73742022-12-011110.12743/quanta.v11i1.19972Clifford Algebras, Spin Groups and Qubit TreesAlexander Yurievich Vlasov0P. V. Ramzaev Research Institute of Radiation Hygiene Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of superfluous branches. The usual Jordan–Wigner construction also may be formally obtained in this approach by bringing the process up to trivial qubit chain (trunk). The methods can also be used for effective simulation of some quantum circuits corresponding to the binary tree structure. The modeling of more general qubit trees, as well as the relationship with the mapping used in the Bravyi–Kitaev transformation, are also briefly discussed. Quanta 2022; 11: 97–114. https://dankogeorgiev.com/ojs/index.php/quanta/article/view/72 |
| spellingShingle | Alexander Yurievich Vlasov Clifford Algebras, Spin Groups and Qubit Trees Quanta |
| title | Clifford Algebras, Spin Groups and Qubit Trees |
| title_full | Clifford Algebras, Spin Groups and Qubit Trees |
| title_fullStr | Clifford Algebras, Spin Groups and Qubit Trees |
| title_full_unstemmed | Clifford Algebras, Spin Groups and Qubit Trees |
| title_short | Clifford Algebras, Spin Groups and Qubit Trees |
| title_sort | clifford algebras spin groups and qubit trees |
| url | https://dankogeorgiev.com/ojs/index.php/quanta/article/view/72 |
| work_keys_str_mv | AT alexanderyurievichvlasov cliffordalgebrasspingroupsandqubittrees |