Fast entangling gates in long ion chains

We present a model for implementing fast entangling gates (∼1μs) with ultrafast pulses in arbitrarily long ion chains, that requires low numbers of pulses and can be implemented with laser repetition rates well within experimental capability. We demonstrate that we are able to optimize pulse sequences that have theoretical fidelities above 99.99% in arbitrarily long ion chains, for laser repetition rates on the order of 100-300 MHz. Notably, we find higher repetition rates are not required for gates in longer ion chains, which is in contrast to scaling analyses with other gate schemes. When pulse imperfections are considered in our calculations, we find that achievable gate fidelity is independent of the number of ions in the chain. We also show that pulse control requirements do not scale up with the number of ions. We find that population transfer efficiencies of above 99.9% from individual ultrafast pulses is the threshold for realizing high-fidelity gates, which may be achievable in near-future experiments.