Influence of a strong pump field on controls of superconducting quantum parametrons

Universal quantum computation and adiabatic quantum computation using parametrons as qubits were proposed and have been studied theoretically and experimentally. A parametron can work as a qubit when it is pumped at approximately twice the natural frequency. A strong pump field can increase T1 decreasing the overlap of two coherent states with opposite phases. However, the pump field of the parametron can be an intrinsic origin of the imperfection of controls because the pump field can disturb the state of parametrons due to the violation of the rotating wave approximation. We report the influence of unwanted rapidly oscillating terms in the Hamiltonian called counter rotating terms (CRTs) on the accuracy of controls of a parametron: a cat-state creation and a single-qubit gate. We also show a method to suppress both of the nonadiabatic transitions and the disturbance of the state of the parametron due to the CRTs.