Extended Data Fig. 1: Experimental system and parameter feedback.

a, Illustration of a Rydberg quantum simulator consisting of strontium-88 atoms trapped in optical tweezers (red funnels). All atoms are driven by a global transverse control field (purple horizontal beam) at a Rabi frequency Ω and a detuning Δ (right panel). The interaction strength is given as \({C}_{6}/{R}_{ij}^{6}\) with an interaction constant C₆ and atomic separations R_ij between two atoms at site i and j. b, Schematic of the experimental feedback scheme. We automatically interleave data taking with feedback to global control parameters and systematic variables through a home-built control architecture (Methods); in particular, we feedback to the clock laser frequency (to maintain optimal state preparation fidelity), the Rydberg laser alignment, the Rydberg detuning Δ, and the Rabi frequency Ω. c, Example of the interleaved automatic Rabi frequency stabilization over the course of ≈ 20 hours with no human intervention. Feedback is comprised of performing single-atom Rabi oscillations, fitting the observed Rabi frequency, and updating the laser amplitude, rather than simply stabilizing the laser amplitude against a photodiode reference. While the Rabi frequency setpoint (orange squares) changes over the course of the sequence (due to long-time instabilities like temperature drifts), the measured Rabi frequency (blue circles) stays constant to within < 0.3%, with a standard deviation of 0.15%. This same stability is seen over the course of multiple days with nearly continuous experimental uptime.