Transform Arbitrary Good Quantum LDPC Codes into Good Geometrically Local Codes in Any Dimension
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914899719880704 |
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| author | Li, Xingjian Lin, Ting-Chun Hsieh, Min-Hsiu |
| author_facet | Li, Xingjian Lin, Ting-Chun Hsieh, Min-Hsiu |
| contents | Geometrically local quantum codes, comprised of qubits and checks embedded in $\mathbb{R}^D$ with local check operators, have been a subject of significant interest. A key challenge is identifying the optimal code construction that maximizes both dimension and distance. Recent advancements have produced several constructions, but these either depend on specific good quantum low-density parity-check (qLDPC) codes or are limited to three dimensions. In this work, we introduce a construction that can transform any good qLDPC code into an optimal geometrically local quantum code. Our approach hinges on a novel procedure that extracts a two-dimensional structure from an arbitrary three-term chain complex. We expect that this procedure will find broader applications in areas such as weight reduction and the geometric realization of chain complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transform Arbitrary Good Quantum LDPC Codes into Good Geometrically Local Codes in Any Dimension Li, Xingjian Lin, Ting-Chun Hsieh, Min-Hsiu Quantum Physics Geometrically local quantum codes, comprised of qubits and checks embedded in $\mathbb{R}^D$ with local check operators, have been a subject of significant interest. A key challenge is identifying the optimal code construction that maximizes both dimension and distance. Recent advancements have produced several constructions, but these either depend on specific good quantum low-density parity-check (qLDPC) codes or are limited to three dimensions. In this work, we introduce a construction that can transform any good qLDPC code into an optimal geometrically local quantum code. Our approach hinges on a novel procedure that extracts a two-dimensional structure from an arbitrary three-term chain complex. We expect that this procedure will find broader applications in areas such as weight reduction and the geometric realization of chain complexes. |
| title | Transform Arbitrary Good Quantum LDPC Codes into Good Geometrically Local Codes in Any Dimension |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.01769 |