Robust Multiparameter Sensing: Randomized Approach

We propose and analyze a versatile multiparameter quantum sensing protocol: it efficiently estimates multiple, mutually non-commuting signals that are coherently or incoherently coupled to sensing particles. Even in the presence of measurement errors, our approach achieves sensitivity scaling as the standard quantum limit. Our approach relies on two key ideas. First, we leverage quantum scrambling to map distinct signals to unique patterns of bitstring measurements, which distinguishes multiple signals without significant sensitivity loss. Second, we utilize classical error correction to mitigate readout errors. We demonstrate our protocol based on global Clifford circuits both analytically and numerically. Furthermore, we extend our framework to local Clifford or Haar-random circuits as well as to ergodic Hamiltonian evolution, which is commonly encountered in quantum hardware. Our work opens the door to a variety of applications, from precise noise benchmarking in quantum dynamics to learning time-dependent Hamiltonians.