Fast Quantum Gates with Electric Field Pulses and Optical Tweezers in Trapped Ions

We propose a two-qubit phase gate based on trapped ions that uses fast electric field pulses and spin-dependent local traps generated by optical tweezers. The phases are engineered by spin-dependent coherent evolution, interspersed with momentum kicks. We derive a set of commensurability conditions and expressions for the spin-dependent accumulated phase that, when satisfied, realize the target two-qubit phase gate within tens of microseconds. We study the scalability of our proposal in larger-ion crystals and demonstrate the existence of solutions with up to four ions. Gates in larger crystals should also be possible but will require more commensurability conditions to be fulfilled.