Methods, systems and apparatus for implementing a quantum gate on a quantum system comprising a second qubit coupled to a first qubit and a third qubit. In one aspect, a method includes evolving a state of the quantum system for a predetermined time, wherein during evolving: the ground and first excited state of the second qubit are separated by a first energy gap ω; the first and second excited state of the second qubit are separated by a second energy gap equal to a first multiple of ω minus qubit anharmoniticity−; the ground and first excited state of the first qubit and third qubit are separated by a third energy gap equal to ω−; and the first and second excited state of the first qubit and third qubit are separated by a fourth energy gap equal to the first multiple of the ω minus a second multiple of .