Universal gate pulse for two-qubit gates on a trapped-ion quantum computer

An ion trap quantum computing system, comprising:

• a quantum processor comprising a first ion chain comprising a plurality of trapped ions, each trapped ion having two hyperfine states and defining a qubit;
• one or more lasers configured to emit a laser beam, which is provided to the plurality of trapped ions in the first ion chain;
• a classical computer configured to perform operations comprising:
• computing a pulse function of a pulse to be applied to a first pair of trapped ions in a second ion chain based on a phase-space condition, wherein the phase-space condition is derived using equi-spaced synthetic frequencies in a frequency interval that includes a range set by a highest and a lowest motional mode frequency of the second ion chain;
• and
• generating the pulse based on the computed pulse function;
• and
• a system controller configured to execute a control program to control the one or more lasers to perform operations on the quantum processor, the operations comprising:
• applying the generated pulse to each of a second pair of trapped ions in the first ion chain to perform an entangling gate operation between the second pair of trapped ions in the first ion chain;
• and
• measuring population of qubit states in the quantum processor,
• wherein the classical computer is further configured to output the measured population of qubit states in the quantum processor.

An ion trap quantum computing system, comprising:

• a classical computer;
• a quantum processor comprising a first ion chain comprising a plurality of trapped ions, each trapped ion having two hyperfine states and defining a qubit;
• a system controller configured to execute a control program to control one or more lasers to perform operations on the quantum processor;
• and
• non-volatile memory having a number of instructions stored therein which, when executed by one or more processors, causes the ion trap quantum computing system to perform operations comprising:
• computing, by the classical computer, a pulse function of a pulse to be applied to a first pair of trapped ions in a second ion chain based on a phase-space condition, wherein the phase-space condition is derived using equi-spaced synthetic frequencies in a frequency interval that includes a range set by a highest and a lowest motional mode frequency of the second ion chain;
• generating, by the classical computer, the pulse based on the computed pulse function;
• applying, by the system controller, the generated pulse to each of a second pair of trapped ions in the first ion chain to perform an entangling gate operation between the second pair of trapped ions in the first ion chain;
• measuring, by the system controller, population of qubit states in the quantum processor;
• and
• outputting, by the classical computer, the measured population of qubit states in the quantum processor.