Non-stop quantum entangling gate between a stationary ion qubit and a mobile one

Towards the arbitrary scalability of a quantum computer, a quantum charge-coupled device (QCCD) based on ion shuttling has currently been regarded as one possible route. However, detaching an ion from and merging it to an ion array and driving non-uniform motion during transportation introduce severe heating issues that cost major overhead in time and laser power for re-cooling and stabilization. To address this issue, we propose a novel entangling scheme between a stationary ion qubit and a non-stopping mobile one, where the latter can be kept in uniform motion without causing heat, and theoretically demonstrate a gate error of the order of magnitude 10^-4 based on current technologies. This scheme enables efficient and economic quantum operations and facilitates long-distance entanglement distribution, where stationary trapped ion arrays form memory units with mobile ions acting as information carriers flying over them, making possible a revolutionary alternative to the QCCD architecture.