  Braiding Majorana zero-modes around each other is a promising route towards
topological quantum computing. Yet, two competing maxims emerge when
implementing Majorana braiding in real systems: On the one hand, perfect
braiding should be conducted adiabatically slowly to avoid non-topological
errors. On the other hand, braiding must be conducted fast such that
decoherence effects introduced by the environment are negligible, which are
generally unavoidable in finite-size systems. This competition results in an
intermediate time scale for Majorana braiding that is optimal, but generally
not error-free. Here, we calculate this intermediate time scale for a
T-junction of short one-dimensional topological superconductors coupled to a
bosonic bath that generates fluctuations in the local electric potential, which
stem from, e.g., environmental photons or phonons of the substrate. We thereby
obtain boundaries for the speed of Majorana braiding with a predetermined gate
fidelity. Our results emphasize the general susceptibility of Majorana-based
information storage in finite-size systems and can serve as a guide for
determining the optimal braiding times in future experiments.
