Two-qubit entangling gate using a continuous spin dependent force coupled with coherent trap manipulation

A quantum information processing (QIP) system, comprising:

• an array of trapped ions including a first trapped ion and a second trapped ion;
• an optical system configured to generate optical beams including a first optical beam applied to the first trapped ion;
• an ion trap configured to trap the first trapped ion and the second trapped ion;
• and
• a controller configured to control operations of the optical system and the ion trap including:
• determining a temporal profile of a trapping potential of the ion trap and obtaining at least one characteristic of the first optical beam to enhance a state dependent phase space displacement to the first trapped ion;
• and
• synchronizing the at least one characteristic of the first optical beam and the temporal profile of the trapping potential and simultaneously applying the first optical beam to the first trapped ion based on the at least one characteristic of the first optical beam and the trapping potential having the temporal profile to the ion trap,
• wherein the optical beams are applied to the first trapped ion and the second trapped ion to implement a two-qubit entangling gate based on the first trapped ion and the second trapped ion.