Fast non-local entangling gates in long ion chains using spin-dependent kicks

We present a theoretical study of fast all-to-all entangling gates in trapped-ion quantum processors, based on impulsive excitation of spin-dependent motion with ultrafast pulsed lasers. Previous studies have shown that such fast gate schemes are highly scalable and naturally performant outside the Lamb-Dicke regime, however are limited to nearest-neighbor operations. Here we demonstrate that impulsive spin-dependent excitation can be used to perform high-fidelity non-local entangling operations in quasi-uniform chains of up to 100 ions. We identify a regime of phonon-mediated entanglement between arbitrary pairs of ions in the chain, where any two pairs of ions in the chain can be entangled in less than two centre-of-mass oscillation periods. We assess the experimental feasibility of the proposed gate schemes, which reveals pulse error requirements that are independent of the length of the ion chain and the distance between the target qubits. Furthermore, we compare the performance of non-local fast gates to equivalent operations composed of sub-microsecond nearest-neighbor gate operations, as well as the achievable performance of spectroscopic protocols employed in existing QCCD and linear-trap architectures. These results suggest entangling gates based on impulsive spin-dependent excitation presents new possibilities for large-scale computation in near-term ion-trap devices.