Phase-estimation optimization in GaAs quantum dots

We address the optimization of phase estimation in the context of GaAs quantum dots [1]. This allows to track the hyperfine field in real time with maximum precision, quenching the main dephasing source. We prove that the mean entropy is the ultimate figure of merit to be minimized for such a purpose, in contrast to the ubiquitous use of the variance in the literature [2,3]. In accordance, non-adaptive and feedback strategies for the tunable interaction times are devised. Whereas global optimization is out of reach, we provide with the optimal offline strategy among the class of memoryless patterns. Remarkably, it indefinitely sustains its maximum precision despite frequency fluctuations and is robust in terms of self consistency. Moreover, we devise a computationally feasible online method to improve the precision for a given non-adaptive strategy, which could be applied to the experimental realization of Kitaev's algorithm. Finally, the scaling of the achieved precision beyond the shot-noise limit is discussed.

[1] M. Delbecq et al., Phys. Rev. Lett. 116, 046802 (2016).
[2] B. L. Higgins et al., Nature 450, 393–396 (2007).
[3] M. Shulman et al., Nat. Comm. 5, 5156 (2014).