Ultrafast gates via state dependent kicks and fast displacements

A quantum information processing (QIP) system, comprising:

• an array of trapped ions including a first trapped ion;
• an optical system configured to generate pairs of optical pulses;
• an ion trap configured to trap the first trapped ion, a trapping potential of the ion trap being switchable between a first trapping potential and a second trapping potential;
• and
• a controller for controlling operations of the optical system and the ion trap, the controller configured to:
• control the optical system to perform a first state dependent kick (SDK) to the first trapped ion that is in a first spin state and a first motional state prior to the first SDK, the first SDK including a first momentum kick to the first trapped ion that depends on the first spin state and is associated with a spin flip from the first spin state into a second spin state, a duration of the first SDK being less than a trap period Ttrap of the first trapped ion;
• and
• switch the first trapping potential of the ion trap to the second trapping potential of the ion trap,
• wherein a phase associated with a current spin state of the first trapped ion is amplified by changing the first trapping potential of the ion trap to the second trapping potential of the ion trap, the phase is dependent on a size of the first momentum kick and the changing of the first trapping potential to the second trapping potential, and the current spin state is one of the first spin state and the second spin state.