We propose a scheme of using two fixed frequency resonator couplers to tune the coupling strength between two Xmon qubits. The induced indirect qubit-qubit interactions by two resonatorscould offset with each other, and the direct coupling between two qubits are not necessarily for switching off. The small direct qubit-quibt coupling could effectively suppress the frequency interval between switching off and switching on, and globally suppress the second and third-order static ZZ couplings. The frequencies differences between resonator couplers and qubits readout resonators are very large, this might be helpful for suppressing the qubits readout errors. The cross-kerr resonant processes between a qubit and two resonators might induce pole and affect the crosstalks between qubits. The double resonator couplers could unfreeze the restrictions on capacitances and coupling strengths in the superconducting circuit, and it can also reduce the flux noises and globally suppress the crosstalks.
With the assistance of a single cyclic three-level system, which can be realized by a superconducting flux qubit, we study theoretically the degenerate microwave parametric down-conversion(PDC) in the superconducting transmission line resonator with the fundamental and second harmonic modes involved. By adiabatically eliminating the excited states of the three-level system, we obtain an effective microwave PDC Hamiltonian for the two modes in the resonator. In our system, the PDC efficiency can be much larger than that in the case of two-level system interacting with two-mode transmission line resonator [K. Moon and S. M. Girvin, Phys. Rev. Lett. {\bf 95}, 140504 (2005)]. With the effective coupling between those two resonator modes, a coherent driving of the second harmonic mode can lead to the squeezing and bunching effect of the fundamental one.
We propose a scheme for generating the Schr“{o}dinger cat state based on geometric operations by a nanomechanical resonator coupled to a superconducting charge qubit. The chargequbit, driven by two strong classical fields, interacts with a high-frequency phonon mode of the nanomechanical resonator. During the operation, the charge qubit undergoes no real transitions, while the phonon mode of the nanomechanical resonator is displaced along different paths in the phase space, dependent on the states of the charge qubit, which yields the Schr\“{o}dinger cat state. The robustness of the scheme is justified by considering noise from environment, and the feasibility of the scheme is discussed.
We propose dynamical schemes to engineer coherent states of a mechanical resonator coupled to an ancillary, superconducting flux qubit. The flux qubit, when repeatedly projected onto its ground state drives the mechanical resonator in to a coherent state in probabilistic, albeit heralded fashion. Assuming no operations on the state of the mechanical resonator during the protocol, coherent states are successfully generated only up to a certain value of the displacement parameter. This restriction can be overcome at the cost of a one-time operation on the initial state of the mechanical resonator. We discuss the possibility of experimental realization of the presented schemes.