Fig. 2: Controlled Overhauser gradient driven rotations of a ST0 qubit by real-time Bayesian estimation.
One loop (solid arrows) represents one repetition of the protocol. a For each repetition, the OPX estimates ΩL by separating a singlet pair for N linearly spaced probe times ti and updating the Bayesian estimate (BE) distribution after each measurement, as shown in the inset of b for one representative repetition. For illustrative purposes, each single-shot measurements mi is plotted as a white/black pixel, here for N = 101 ΩL probe cycles, and the fraction of singlet outcomes in each column is shown as a red dot. b Probability distribution P(ΩL) after completion of each repetition in a. Extraction of the expected value 〈ΩL〉 from each row completes ΩL estimation. c For each repetition, unless 〈ΩL〉 falls below a user-defined minimum (here 50 MHz), the OPX adjusts the separation times \({\tilde{t}}_{j}\), using its real-time knowledge of 〈ΩL〉, to rotate the qubit by user-defined target angles \({\theta }_{j}={\tilde{t}}_{j}\,\langle {{{\Omega }}}_{{{{{{{{\rm{L}}}}}}}}}\rangle\). d To illustrate the increased coherence of Overhauser gradient driven rotations, we task the OPX to perform M = 80 evenly spaced θj rotations. Single-shot measurements mj are plotted as white/black pixels, and the fraction of singlet outcomes in each column is shown as a red dot.
