Loss in hybrid qubit-bus couplings and gates

We provide a characterization and analysis of the effects of dissipation on oscillator assisted (qubus) quantum gates. The effects can be understood and minimized by looking at the dynamics of the signal coherence and its entanglement with the continuous variable probe. Adding loss in between successive interactions we obtain the effective quantum operations, providing a novel approach to loss analysis in such hybrid settings. We find that in the presence of moderate dissipation the gate can operate with a high fidelity. We also show how a simple iteration scheme leads to independent single qubit dephasing, while retaining the conditional phase operation regardless of the amount of loss incurred by the probe.