Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes (‘quasi codes’). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The mod...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2022-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ac4737 |
| _version_ | 1797748470109437952 |
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| author | Dong-Sheng Wang Yun-Jiang Wang Ningping Cao Bei Zeng Raymond Laflamme |
| author_facet | Dong-Sheng Wang Yun-Jiang Wang Ningping Cao Bei Zeng Raymond Laflamme |
| author_sort | Dong-Sheng Wang |
| collection | DOAJ |
| description | In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes (‘quasi codes’). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation. |
| first_indexed | 2024-03-12T16:06:13Z |
| format | Article |
| id | doaj.art-10cf8cc9f9c840bc96afe18cf1d49d81 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:06:13Z |
| publishDate | 2022-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-10cf8cc9f9c840bc96afe18cf1d49d812023-08-09T14:20:23ZengIOP PublishingNew Journal of Physics1367-26302022-01-0124202301910.1088/1367-2630/ac4737Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codesDong-Sheng Wang0Yun-Jiang Wang1Ningping Cao2Bei Zeng3Raymond Laflamme4CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences , Beijing 100190, People’s Republic of China; Institute for Quantum Computing, University of Waterloo , Waterloo, Ontario N2L 3G1, CanadaState Key Laboratory of Integrated Services Networks, Xidian University , Xian, Shaanxi, People’s Republic of ChinaInstitute for Quantum Computing, University of Waterloo , Waterloo, Ontario N2L 3G1, Canada; Department of Mathematics and Statistics, University of Guelph , Guelph, Ontario N1G 2W1, CanadaDepartment of Physics, The Hong Kong University of Science and Technology , Clear Water Bay, Kowloon, Hong Kong, People’s Republic of ChinaInstitute for Quantum Computing, University of Waterloo , Waterloo, Ontario N2L 3G1, Canada; Department of Physics and Astronomy, University of Waterloo , Waterloo, Ontario N2L 3G1, CanadaIn this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes (‘quasi codes’). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.https://doi.org/10.1088/1367-2630/ac4737quantum computationsymmetry-protected topological orderquantum error correction |
| spellingShingle | Dong-Sheng Wang Yun-Jiang Wang Ningping Cao Bei Zeng Raymond Laflamme Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes New Journal of Physics quantum computation symmetry-protected topological order quantum error correction |
| title | Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes |
| title_full | Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes |
| title_fullStr | Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes |
| title_full_unstemmed | Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes |
| title_short | Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes |
| title_sort | theory of quasi exact fault tolerant quantum computing and valence bond solid codes |
| topic | quantum computation symmetry-protected topological order quantum error correction |
| url | https://doi.org/10.1088/1367-2630/ac4737 |
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