Fault-tolerant dynamically-decoupled hyper-Ramsey spectroscopy of ultra-narrow clock transitions

Hyper-Ramsey protocols effectively reduce AC-Stark shifts in probing ultra-narrow optical clock transitions but they remain sensitive to laser intensity noise, decoherence, frequency drifts, and low-frequency perturbations. We address these limitations by incorporating dynamical decoupling, using sequences of rotary Hahn-echo pulses that toggle the probe frequency detuning and phase between opposite signs. Implementing time-optimized Eulerian cycling circuits of multiple refocusing pulses, we generate high-contrast hyper-Ramsey interferences that are completely free from AC-Stark shifts and robust against environmental noise and laser probe parameters imperfections. We demonstrate the robustness of our dynamically-decoupled hyper-Ramsey interrogation scheme by implementing it directly at the pulse level on a superconducting quantum processing unit. Fault tolerant dynamically-decoupled SU(2) hyper-clocks are a significant step toward universal, noise resilient quantum sensors, enabling fault-tolerant metrology for searches about new physics beyond the Standard Model.