Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics

Based on a microwave-photon quantum processor with multiple superconducting resonators coupled to one three-level superconducting qutrit, we construct the controlled-phase (c-phase) and controlled-controlled-phase (cc-phase) gates on microwave-photon-resonator qudits, by combination of the photon-number-dependent frequency-shift effect and the resonant operation between the qutrit and a resonator. This distinct feature provides us a useful way for achieving higher fidelity quantum logic gates on resonator qudits in a shorter operation time, compared with others. The fidelity of our c-phase gate can reach 99.51% within 92 ns. The fidelity of our cc-phase gate on three resonator qudits constructed here in the first time, can reach 92.92% within 124.64 ns.