  Based on a microwave-photon quantum processor with two superconducting
resonators coupled to one transmon qutrit, we construct the controlled-phase
(c-phase) gate on microwave-photon-resonator qudits, by combination of the
photon-number-dependent frequency-shift effect on the transmon qutrit by the
first resonator and the resonant operation between the qutrit and the second
resonator. This distinct feature provides us a useful way to achieve the
c-phase gate on the two resonator qudits with a higher fidelity and a shorter
operation time, compared with the previous proposals. The fidelity of our
c-phase gate can reach 99.51% within 93 ns. Moreover, our device can be
extended easily to construct the three-qudit gates on three resonator qudits,
far different from the existing proposals. Our controlled-controlled-phase gate
on three resonator qudits is accomplished with the assistance of a transmon
qutrit and its fidelity can reach 92.92% within 124.64 ns.
