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Paper 1
Fiber Bundle Fault Tolerance of GKP Codes
Ansgar G. Burchards, Steven T. Flammia, Jonathan Conrad
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.07332
- arXiv
- 2410.07332
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.
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