  Achieving high-fidelity direct two-qubit gates over meter-scale long quantum
interconnects is challenging in part due to the multimode nature of such
systems. One alternative scheme is to combine local operations with remote
quantum state transfer or remote entanglement. Here, we study quantum state
transfer and entanglement generation for two distant qubits, equipped with
tunable interactions, over a common multimode interconnect. We employ the
SuperAdiabatic Transitionless Driving (SATD) solutions for adiabatic passage
and demonstrate various favorable improvements over the standard protocol. In
particular, by suppressing leakage to a select (resonant) interconnect mode,
SATD breaks the speed-limit relation imposed by the qubit-interconnect
interaction $g$, where instead the operation time is limited by leakage to the
adjacent modes, i.e. free spectral range $\Delta_c$ of the interconnect,
allowing for fast operations even with weak $g$. Furthermore, we identify a
multimode error mechanism for Bell state generation using such adiabatic
protocols, in which the even/odd modal dependence of qubit-interconnect
interaction breaks down the dark state symmetry, leading to detrimental
adiabatic overlap with the odd modes growing as $(g/\Delta_c)^2$. Therefore,
adopting a weak coupling, imposed by a multimode interconnect, SATD provides a
significant improvement in terms of operation speed and consequently
sensitivity to incoherent error.
