Almost Linear Decoder for Optimal Geometrically Local Quantum Codes
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913923300589568 |
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| author | Eggerickx, Quinten Wills, Adam Lin, Ting-Chun De Greve, Kristiaan Hsieh, Min-Hsiu |
| author_facet | Eggerickx, Quinten Wills, Adam Lin, Ting-Chun De Greve, Kristiaan Hsieh, Min-Hsiu |
| contents | Geometrically local quantum codes, which are error correction codes embedded in $\mathbb{R}^D$ 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 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02928 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost Linear Decoder for Optimal Geometrically Local Quantum Codes Eggerickx, Quinten Wills, Adam Lin, Ting-Chun De Greve, Kristiaan Hsieh, Min-Hsiu Quantum Physics Geometrically local quantum codes, which are error correction codes embedded in $\mathbb{R}^D$ 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 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. |
| title | Almost Linear Decoder for Optimal Geometrically Local Quantum Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.02928 |