Replacing quantum feedback with open-loop control and quantum filtering

Feedback control protocols can stabilize and enhance the operation of quantum devices, however, unavoidable delays in the feedback loop adversely affect their performance. We introduce a quantum control methodology, combining open-loop control with quantum filtering, which is not constrained by feedback delays. For the problems studied (rapid purification and rapid measurement) we analytically derive lower bounds on the control performance that are comparable with the best corresponding bounds for feedback protocols.

Figure 1

A schematic of important time scales in a feedback loop. For devices, the times depicted are the reciprocals of the component bandwidths. The ${\tau }_{\mathrm{el}}^i$’s are electronic delays between devices. The total effective delay is: ${\tau }_{\mathrm{del}}\equiv {\sum }_i{\tau }_{\mathrm{el}}^i+{\tau }_{\det }+{\tau }_{\mathrm{fil}}+{\tau }_{\mathrm{ctrl}}$.

Figure 2

The purification speed-up provided by the random unitary strategy for $D=4$. The solid curve is a lower bound on the speed-up in the limit where the time $\delta t$ between unitary controls goes to zero, as explained below (7), and the dashed line is its asymptotic (high-purity) limit. The circles, squares, and triangles are numerical calculations of the speed-up with finite $\delta t=0.01$, $0.25$, and $1$ (in units of the reciprocal measurement rate), respectively.

Figure 3

The speed-up for permutation strategies for $D=4$. The dashed lines are the asymptotic bounds in Eq. (12). The results for random permutation strategy are shown by circles for $\delta t=6.25\times {10}^{-4}{\gamma }^{-1}$ and triangles for $\delta t=1.25\times {10}^{-3}{\gamma }^{-1}$. The squares are for the deterministic strategy described in the text with $\delta t=6.25\times {10}^{-4}{\gamma }^{-1}$.