Composable logical gate error in approximate quantum error correction: reexamining gate implementations in Gottesman-Kitaev-Preskill codes
This research introduces a new measure, composable logical gate error, to rigorously quantify inaccuracies in approximate quantum error correction gates. It shows this error is subadditive under sequential operations and provides bounds based on matrix elements of physical implementations. For GKP codes using linear optics, it finds that Pauli gate errors improve with squeezing but phase gate errors remain fundamentally limited.