Almost linear decoder for optimal geometrically local quantum codes
Geometrically local quantum codes, which are error-correction codes embedded in R^{D} with checks acting only on qubits within a fixed spatial distance, have garnered significant interest. Recently, it has been demonstrated how to achieve geometrically local codes that maximize both the dimension an...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-06-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/sxdx-qbcz |
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| _version_ | 1849683747674259456 |
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| author | Quinten Eggerickx Adam Wills Ting-Chun Lin Kristiaan De Greve Min-Hsiu Hsieh |
| author_facet | Quinten Eggerickx Adam Wills Ting-Chun Lin Kristiaan De Greve Min-Hsiu Hsieh |
| author_sort | Quinten Eggerickx |
| collection | DOAJ |
| description | Geometrically local quantum codes, which are error-correction codes embedded in R^{D} with checks acting only on qubits within a fixed spatial distance, have garnered significant interest. Recently, it has been demonstrated how to achieve geometrically local codes that maximize both the dimension and the distance, as well as the energy barrier of the code. In this work, we focus on the constructions involving subdivision, and we show that they have an almost linear time decoder, obtained by combining the decoder of the outer good qLDPC code and a generalized version of the Union-Find decoder. This provides the first decoder for an optimal geometrically local three-dimensional code. We demonstrate the existence of a finite threshold error rate under the code capacity noise model using a minimum weight perfect matching decoder. Furthermore, we argue that this threshold is also applicable to the decoder based on the generalized Union-Find algorithm. |
| format | Article |
| id | doaj-art-ca6ae27a40be490d98c6b3231fc62e92 |
| institution | DOAJ |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-ca6ae27a40be490d98c6b3231fc62e922025-08-20T03:23:43ZengAmerican Physical SocietyPhysical Review Research2643-15642025-06-017202330010.1103/sxdx-qbczAlmost linear decoder for optimal geometrically local quantum codesQuinten EggerickxAdam WillsTing-Chun LinKristiaan De GreveMin-Hsiu HsiehGeometrically local quantum codes, which are error-correction codes embedded in R^{D} with checks acting only on qubits within a fixed spatial distance, have garnered significant interest. Recently, it has been demonstrated how to achieve geometrically local codes that maximize both the dimension and the distance, as well as the energy barrier of the code. In this work, we focus on the constructions involving subdivision, and we show that they have an almost linear time decoder, obtained by combining the decoder of the outer good qLDPC code and a generalized version of the Union-Find decoder. This provides the first decoder for an optimal geometrically local three-dimensional code. We demonstrate the existence of a finite threshold error rate under the code capacity noise model using a minimum weight perfect matching decoder. Furthermore, we argue that this threshold is also applicable to the decoder based on the generalized Union-Find algorithm.http://doi.org/10.1103/sxdx-qbcz |
| spellingShingle | Quinten Eggerickx Adam Wills Ting-Chun Lin Kristiaan De Greve Min-Hsiu Hsieh Almost linear decoder for optimal geometrically local quantum codes Physical Review Research |
| title | Almost linear decoder for optimal geometrically local quantum codes |
| title_full | Almost linear decoder for optimal geometrically local quantum codes |
| title_fullStr | Almost linear decoder for optimal geometrically local quantum codes |
| title_full_unstemmed | Almost linear decoder for optimal geometrically local quantum codes |
| title_short | Almost linear decoder for optimal geometrically local quantum codes |
| title_sort | almost linear decoder for optimal geometrically local quantum codes |
| url | http://doi.org/10.1103/sxdx-qbcz |
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