Fiber Bundle Fault Tolerance of GKP Codes
arXiv:2410.07332 · doi:10.22331/q-2025-10-29-1899
Abstract
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.
16 pages (14 main + 2 appendices)
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