  We study the coupling between Majorana bound states (CMBS), which is mediated
by a topologically trivial chain in the presence of pairing coupling and
long-range coupling. The results show that CMBS can be enhanced by the pairing
coupling and long-range coupling of the trivial chain. When driving the trivial
chain by periodic driving field, we deduce the analytical expressions of CMBS
in the high-frequency limit, and demonstrate that CMBS can be modulated by the
frequency and amplitude of driving field. Finally we exhibit the application of
tunable CMBS in realizing quantum logic gates.
