Fast, high-fidelity, QND measurements of superconducting qubits using a transverse interaction?

The standard procedure for measuring superconducting qubits is to couple them to a cavity mode via a tranverse interaction, and to detune the cavity from the qubit to obtain an effective "dispersive" interaction in which the qubit shifts the frequency of the cavity. This allows the state of the qubit to be read out by measuring the phase shift of a signal that is passed through the cavity. This technique is often referred to as providing a quantum non-demolition (QND) measurement, since the effective dispersive interaction has the QND form, but in fact it will only approximate a QND measurement to any reasonable degree when used with a detuning so large as to significantly reduce the effective interaction strength and thus the measurement speed. As a result, measurements that use this technique so as to achieve state-of-the-art speeds (e.g., below 100 ns) are not operated in the QND regime. Here we show that there is signifcantly more to understand about the transverse interaction than the received wisdom that we have just described. In particualr we show that by using a circuit configuration in which the qubit/cavity interaction strength can be controlled in a time-dependent fashion, and by carefully choosing the time-envelope of this strength, it is possible to exploit a recurrance phenomena in the transferverse interaction to acheive fast QND measurements. This technique appears to be quite feasible even though it requires fairly precise control. We will discuss a circuit design that could be used to implement it as well as some further properties of the transverse interaction.