Layer codes
Abstract Quantum computers require memories that are capable of storing quantum information reliably for long periods of time. The surface code is a two-dimensional quantum memory with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional lo...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-11-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-024-53881-3 |
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| _version_ | 1846171728740352000 |
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| author | Dominic J. Williamson Nouédyn Baspin |
| author_facet | Dominic J. Williamson Nouédyn Baspin |
| author_sort | Dominic J. Williamson |
| collection | DOAJ |
| description | Abstract Quantum computers require memories that are capable of storing quantum information reliably for long periods of time. The surface code is a two-dimensional quantum memory with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet optimal code was not previously known. Here we present a family of three dimensional topological codes with optimal scaling code parameters and a polynomial energy barrier. Our codes are based on a construction that takes in a stabilizer code and outputs a three-dimensional topological code with related code parameters. The output codes are topological defect networks formed by layers of surface code joined along one-dimensional junctions, with a maximum stabilizer check weight of six. When the input is a family of good quantum low-density parity-check codes the output codes have optimal scaling. Our results uncover strongly-correlated states of quantum matter that are capable of storing quantum information with the strongest possible protection from errors that is achievable in three dimensions. |
| format | Article |
| id | doaj-art-3c871b18d768461283a87b451690fad2 |
| institution | Kabale University |
| issn | 2041-1723 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-3c871b18d768461283a87b451690fad22024-11-10T12:34:23ZengNature PortfolioNature Communications2041-17232024-11-011511710.1038/s41467-024-53881-3Layer codesDominic J. Williamson0Nouédyn Baspin1Centre for Engineered Quantum Systems, School of Physics, University of SydneyCentre for Engineered Quantum Systems, School of Physics, University of SydneyAbstract Quantum computers require memories that are capable of storing quantum information reliably for long periods of time. The surface code is a two-dimensional quantum memory with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet optimal code was not previously known. Here we present a family of three dimensional topological codes with optimal scaling code parameters and a polynomial energy barrier. Our codes are based on a construction that takes in a stabilizer code and outputs a three-dimensional topological code with related code parameters. The output codes are topological defect networks formed by layers of surface code joined along one-dimensional junctions, with a maximum stabilizer check weight of six. When the input is a family of good quantum low-density parity-check codes the output codes have optimal scaling. Our results uncover strongly-correlated states of quantum matter that are capable of storing quantum information with the strongest possible protection from errors that is achievable in three dimensions.https://doi.org/10.1038/s41467-024-53881-3 |
| spellingShingle | Dominic J. Williamson Nouédyn Baspin Layer codes Nature Communications |
| title | Layer codes |
| title_full | Layer codes |
| title_fullStr | Layer codes |
| title_full_unstemmed | Layer codes |
| title_short | Layer codes |
| title_sort | layer codes |
| url | https://doi.org/10.1038/s41467-024-53881-3 |
| work_keys_str_mv | AT dominicjwilliamson layercodes AT nouedynbaspin layercodes |