  We propose a simple scheme for implementing fast arbitrary phase gates and
employ pulse modulation to improve the gate robustness against different
sources of noise. Parametric driving of a cavity is introduced to induce Rabi
interactions between the cavity and qutrits, and then a two-qubit arbitrary
phase gate is constructed by designing proper logical states. On this basis, we
implement amplitude-shaped gates to obtain enhanced resilience to control
errors in gate time and frequency detuning. By virtue of specifically designed
logical states, the scheme displays intrinsic resistance to the energy
relaxations of qutrits. Furthermore, we show that the gate robustness against
cavity decay can be enhanced significantly with amplitude modulation.
