A method of performing quantum operations in a trapped-ion quantum system, comprising: implementing two parallel gates of a quantum circuit, each of the two parallel gates being a 2-qubit gate, each of the two parallel gates being implemented using a different set of ions of a plurality of ions in an ion trap, the two parallel gates including a first 2-qubit gate implemented using a first set of ions and a second 2-qubit gate implemented using a second set of ions, the first set of ions and the second set of ions being entangled sets and any remaining sets of ions of the plurality of ions in the ion trap are not entangled sets, wherein implementing the two parallel gates includes generating a first optical pulse sequence and applying to the first set of ions first beams based on the first optical pulse sequence to implement the first gate, a solution of the first optical pulse sequence being based on quadratic entanglement constraints and having multiple segments, each segment of the first pulse sequence corresponding to a relative frequency during that segment of the first gate, and the segments of the first pulse sequence being of equal duration, and wherein implementing the two parallel gates includes generating a second pulse sequence and applying to the second set of ions second beams based on the second optical pulse sequence to implement the second gate, a solution of the second pulse sequence being based on quadratic entanglement constraints and having multiple segments for the second gate, each segment of the second pulse sequence corresponding to a relative frequency during that segment of the second gate, and the segments of the second pulse sequence being of equal duration; and simultaneously performing operations on the two parallel gates as part of the quantum operations. implementing two parallel gates of a quantum circuit, each of the two parallel gates being a 2-qubit gate, each of the two parallel gates being implemented using a different set of ions of a plurality of ions in an ion trap, the two parallel gates including a first 2-qubit gate implemented using a first set of ions and a second 2-qubit gate implemented using a second set of ions, the first set of ions and the second set of ions being entangled sets and any remaining sets of ions of the plurality of ions in the ion trap are not entangled sets, wherein implementing the two parallel gates includes generating a first optical pulse sequence and applying to the first set of ions first beams based on the first optical pulse sequence to implement the first gate, a solution of the first optical pulse sequence being based on quadratic entanglement constraints and having multiple segments, each segment of the first pulse sequence corresponding to a relative frequency during that segment of the first gate, and the segments of the first pulse sequence being of equal duration, and wherein implementing the two parallel gates includes generating a second pulse sequence and applying to the second set of ions second beams based on the second optical pulse sequence to implement the second gate, a solution of the second pulse sequence being based on quadratic entanglement constraints and having multiple segments for the second gate, each segment of the second pulse sequence corresponding to a relative frequency during that segment of the second gate, and the segments of the second pulse sequence being of equal duration; and simultaneously performing operations on the two parallel gates as part of the quantum operations. <EOS>