Supplemental Material to ” Shortcuts to nonabelian braiding ”

Note that both the eigen-Majoranas γn,α and the eigenvalues n are time dependent. Degeneracies of the many-body spectrum can arise when one or more of the eigenvalues n vanish or when some nonzero n is degenerate, independent of time. The various Majorana operators associated with each single-particle eigenvalue n are labeled by the index α. If the single-particle eigenvalue n is N-fold degenerate, α takes on 2N different values, α = 1, . . . , 2N. A direct derivation of the counterdiabatic terms based on the general Eq. (12) in the main text is cumbersome. Here, we choose to proceed as follows. The counterdiabatic terms suppress transitions out of the degenerate subspace but leave the dynamics within the degenerate subspace as governed by the nonabelian Berry connection of the original time evolution unchanged. Thus, we can determine the counterdiabatic terms H1 uniquely from the following constraints: (a) H1 has no matrix elements which act within the degenerate eigenspaces of H0. This ensures that H1 affects only transitions between states with different energies.