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arXiv · 2410.07332

Fiber Bundle Fault Tolerance of GKP Codes

Ansgar G. Burchards·Steven T. Flammia·Jonathan Conrad
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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.

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Ansgar G. Burchards, Steven T. Flammia, Jonathan Conrad. 2025-10-07. Fiber Bundle Fault Tolerance of GKP Codes. https://doi.org/10.22331/q-2025-10-29-1899

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