Enhanced quantum state transfer and Bell-state generation over long-range multimode interconnects via superadiabatic transitionless driving

Achieving high-fidelity direct two-qubit gates over meter-scale 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 theoretically study quantum state transfer and entanglement generation for two distant qubits, equipped with tunable interactions, over a common multimode interconnect. We model the performance of the superadiabatic transitionless driving (SATD) protocol for adiabatic passage and demonstrate various favorable improvements over the standard method. 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., the free spectral range ${\mathrm{\Delta }}_c$ 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 $(g/{\mathrm{\Delta }}_c{)}^2$. 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.