Time- and Photon-Optimal Paths for the Preparation and Logical Flip of Gottesman-Kitaev-Preskill States

arXiv:2611.15018v1 Announce Type: new Abstract: Gottesman-Kitaev-Preskill (GKP) states are highly non-Gaussian, making their control challenging, particularly in the presence of photon loss. Here, we use the brachistochrone, the fastest path at bounded speed, to construct ideal nonlinear Hamiltonians for state preparation and logical gates, and compare it with the photon-optimal path. We find that the two paths nearly coincide for state preparation but differ markedly for logical operations, namely the brachistochrone preserves the encoded qubit during a bit flip, whereas the photon-optimal path flips a known state through the vacuum. We then introduce the tangential capacity to quantify how effectively gate sets track these paths.