One-step implementation of a hybrid discrete-variable–continuous-variable phase gate with multiple photonic qubits in circuit QED

Quantum phase gates are of fundamental interest in quantum physics and play an important role in quantum communication and quantum computing. Here, we propose a scheme to implement a hybrid discrete-variable–continuous-variable (DV–CV) phase gate on multiple photonic qubits by utilizing multiple control microwave cavities and a single target microwave cavity, all coupled to a common superconducting qutrit (a three-level quantum system) in circuit quantum electrodynamics (QED). In our scheme, two logic states of the target qubit are encoded via the vacuum state and the coherent state (CV state) of the microwave cavity, while two logic states of the control qubits are encoded through the vacuum and single-photon states (DV states) of the microwave cavity. This hybrid DV–CV phase gate enables target qubit to acquire a phase that depends on the total number of control qubits in non-vacuum states, when the target qubit is in the coherent state. Our protocol is extensible and operationally efficient, involving just one step and the measurement of only one target qubit. In addition, as a practical application, this hybrid DV–CV phase gate can be employed as a quantum voting machine. Our numerical simulation demonstrates that the high-fidelity construction of a hybrid three-qubit DV–CV phase gate is feasible with current circuit QED technology.