Information-Scrambling-Enhanced Quantum Sensing Beyond the Standard Quantum Limit

Abstract: Quantum sensing promises measurement precision beyond classical limits, but its practical realization is often hindered by decoherence and the challenges of generating and stabilizing entanglement in large-scale systems. Here, we experimentally demonstrate a scalable, scrambling-enhanced quantum sensing protocol, referred to as butterfly metrology, implemented on a cross-shaped superconducting quantum processor. By harnessing quantum information scrambling, the protocol converts local interactions into delocalized metrologically useful correlations, enabling robust signal amplification through interference of the scrambled and polarized quantum states. We validate the time-reversal ability via Loschmidt echo measurements and quantify the information scrambling through out-of-time-ordered correlators, establishing the essential quantum resources of our protocol. Our measurements reveal that the sensing sensitivity surpasses the standard quantum limit (SQL) with increasing qubit number, reaching 3.78 in a 9-qubit configuration, compared to the SQL of 3.0. The scheme further exhibits inherent robustness to coherent control errors and probed signal noise. This work demonstrates a readily scalable path toward practical quantum sensing advantages with prevalent experimental platforms.