Unitary-Feedback-Improved Qubit Initialization in the Dispersive Regime

The read-out of the state of a superconducting qubit by homodyne detection of the output signal from a dispersively coupled microwave resonator is a common technique in circuit quantum electrodynamics and is often claimed to be quantum nondemolition (QND) up to the same order of approximation as that of the dispersive approximation. However, in this work we show that only in the limit of infinite measurement time is this protocol QND, as the formation of a dressed coherent state in the qubit-cavity system applies an effective rotation to the qubit state. We show how this rotation can be corrected by a unitary operation, leading to improved qubit initialization by measurement and unitary feedback.

Figure 1

(a) Cavity occupation and (b) $1-P(t)$ for $T=0$ and $T=100\mathrm{mK}$ for both initial states. $1-{\mathcal{F}}_{\nu }(\tau )$ and $1-{\mathcal{F}}_{\nu }^C(\tau )$ are shown in (c) for $T=0$ and (d) for $T=100\mathrm{mK}$. A drive strength of $|\epsilon |/2\pi =0.04\mathrm{GHz}$, a cavity decay rate of $1/\kappa =100\mathrm{ns}$, and $|\lambda |=0.1$ are used for these simulations.

Figure 2

$1-{\mathcal{F}}_{\nu }(\tau )$ and $1-{\mathcal{F}}_{\nu }^C(\tau )$ for $T=0$. A drive strength of $|\epsilon |/2\pi =0.04\mathrm{GHz}$, a cavity decay rate of $1/\kappa =100\mathrm{ns}$, and $|\lambda |=0.1$ are used for this simulation.