Qubit Regularization and Qubit Embedding Algebras
Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preser...
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MDPI AG
2022-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/2/305 |
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| author | Hanqing Liu Shailesh Chandrasekharan |
| author_facet | Hanqing Liu Shailesh Chandrasekharan |
| author_sort | Hanqing Liu |
| collection | DOAJ |
| description | Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the O<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></semantics></math></inline-formula> lattice spin models and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">SU</mo><mo>(</mo><mi>N</mi><mo>)</mo></mrow></semantics></math></inline-formula> lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories. |
| first_indexed | 2024-03-09T20:57:12Z |
| format | Article |
| id | doaj.art-2e880b4758d747449bfe25606728b78e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T20:57:12Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2e880b4758d747449bfe25606728b78e2023-11-23T22:16:28ZengMDPI AGSymmetry2073-89942022-02-0114230510.3390/sym14020305Qubit Regularization and Qubit Embedding AlgebrasHanqing Liu0Shailesh Chandrasekharan1Department of Physics, Duke University, Durham, NC 27708, USADepartment of Physics, Duke University, Durham, NC 27708, USAQubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the O<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></semantics></math></inline-formula> lattice spin models and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">SU</mo><mo>(</mo><mi>N</mi><mo>)</mo></mrow></semantics></math></inline-formula> lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.https://www.mdpi.com/2073-8994/14/2/305lattice spin modelslattice gauge theoriesquantum computation/simulationquantum criticality |
| spellingShingle | Hanqing Liu Shailesh Chandrasekharan Qubit Regularization and Qubit Embedding Algebras Symmetry lattice spin models lattice gauge theories quantum computation/simulation quantum criticality |
| title | Qubit Regularization and Qubit Embedding Algebras |
| title_full | Qubit Regularization and Qubit Embedding Algebras |
| title_fullStr | Qubit Regularization and Qubit Embedding Algebras |
| title_full_unstemmed | Qubit Regularization and Qubit Embedding Algebras |
| title_short | Qubit Regularization and Qubit Embedding Algebras |
| title_sort | qubit regularization and qubit embedding algebras |
| topic | lattice spin models lattice gauge theories quantum computation/simulation quantum criticality |
| url | https://www.mdpi.com/2073-8994/14/2/305 |
| work_keys_str_mv | AT hanqingliu qubitregularizationandqubitembeddingalgebras AT shaileshchandrasekharan qubitregularizationandqubitembeddingalgebras |