Amplitude modulated pulses for implementation of entangling gates in ion trap quantum computers

A quantum computing system, comprising:

• a plurality of trapped ions, each of the trapped ions having two hyperfine states defining a qubit;
• and
• a classical computer comprising non-volatile memory having a number of instructions stored therein which, when executed by a processor, causes the quantum computing system to perform operations comprising:
• configuring an amplitude function of an amplitude-modulated laser pulse over a plurality of time segments to cause entangling interaction between a pair of trapped ions of a plurality of trapped ions, each of the plurality of trapped ions having two frequency-separated states defining a qubit, wherein the amplitude function in each time segment is splined using a set of basis functions and associated control parameters;
• and
• performing an entangling gate operation between the pair of trapped ions by applying, by a system controller, an amplitude-modulated laser pulse having the configured amplitude function to the pair of trapped ions.