Balanced coupling in superconducting circuits

The rotating wave approximation (RWA) is ubiquitous in the analysis of driven and coupled resonators. However, the limitations of the RWA seem to be poorly understood and in some cases the RWA disposes of essential physics. We investigate the RWA in the context of electrical resonant circuits. Using a classical Hamiltonian approach, we find that by balancing electrical and magnetic components of the resonator drive or resonator-resonator coupling, the RWA can be made to be exact. This type of balance, in which the RWA is exact, has applications in superconducting circuits where it suppresses single qubit gate error in qubits with very low frequencies, and may suppress deleterious qubit transitions caused by dispersive readout.