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Lattices, Gates, and Curves: GKP codes as a Rosetta stone

Conrad, Jonathan et al.
arXiv (All) · Papers
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algebraic-geometrydifferential-geometrygeometric-topologymathematical-physicsquantum-physics
We explain how GKP Clifford gates arise as symplectic automorphisms of the corresponding GKP lattice and show that, for scaled codes of type $D=dI_n$, their integral action agrees with the action of the mapping class group of a genus-$n$ surface on first homology. This correspondence introduces a to
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