On-Device Learning of Optimal Probes via Out-of-Time-Order Correlators in Noise-Adaptive Quantum Metrology

Quantum metrology promises to surpass classical precision limits by leveraging quantum resources such as entanglement. Maximally entangled Greenberger-Horne-Zeilinger (GHZ) states are theoretically optimal probes for quantum metrology. However, they are fragile to environmental noise, severely limiting their practical utility. To overcome this limitation, we propose and experimentally realize a noise-adaptive quantum metrology scheme that autonomously identifies optimal probes without any prior information of the noise. This is achieved by combining a variational quantum circuit that optimizes available resources with an efficient strategy for evaluating the sensing performance. Using a seven-qubit nuclear spin sensor, we identify optimal probe states that achieve precision improvements up to 0.698 dB over GHZ states when sensing a fixed magnetic field. Furthermore, we show that the learned probe state exhibits cross-parameter robustness, maintaining superior performance over a broad range of magnetic field frequencies. The proposed scheme is model-free, hardware-efficient, and scalable, providing a practical route to noise-resilient quantum metrology on near-term quantum devices.