Fiber Bundle Fault Tolerance of GKP Codes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908617372860416 |
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| author | Burchards, Ansgar G. Flammia, Steven T. Conrad, Jonathan |
| author_facet | Burchards, Ansgar G. Flammia, Steven T. Conrad, Jonathan |
| contents | We investigate multi-mode GKP (Gottesman--Kitaev--Preskill) quantum error-correcting codes from a geometric perspective. First, we construct their moduli space as a quotient of groups and exhibit it as a fiber bundle over the moduli space of symplectically integral lattices. We then establish the Gottesman--Zhang conjecture for logical GKP Clifford operations, showing that all such gates arise from parallel transport with respect to a flat connection on this space. Specifically, non-trivial Clifford operations correspond to topologically non-contractible paths on the space of GKP codes, while logical identity operations correspond to contractible paths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fiber Bundle Fault Tolerance of GKP Codes Burchards, Ansgar G. Flammia, Steven T. Conrad, Jonathan Quantum Physics We investigate multi-mode GKP (Gottesman--Kitaev--Preskill) quantum error-correcting codes from a geometric perspective. First, we construct their moduli space as a quotient of groups and exhibit it as a fiber bundle over the moduli space of symplectically integral lattices. We then establish the Gottesman--Zhang conjecture for logical GKP Clifford operations, showing that all such gates arise from parallel transport with respect to a flat connection on this space. Specifically, non-trivial Clifford operations correspond to topologically non-contractible paths on the space of GKP codes, while logical identity operations correspond to contractible paths. |
| title | Fiber Bundle Fault Tolerance of GKP Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.07332 |