According to some aspects, a method is provided of operating a circuit quantum electrodynamics system that includes a physical qubit dispersively coupled to a quantum mechanical oscillator, the method comprising applying a first electromagnetic pulse to the physical qubit based on a number state of the quantum mechanical oscillator, wherein the first electromagnetic pulse causes a change in state of the quantum mechanical oscillator, and applying, subsequent to application of the first electromagnetic pulse, a second electromagnetic pulse to the quantum mechanical oscillator that coherently adds or removes energy from the quantum mechanical oscillator.