Shallow randomized measurement in noisy quantum devices

Quantum hardware is steadily improving, but near-term quantum devices remain limited by noise and circuit depth. This motivates measurement protocols that can use shallow-depth circuits while remaining robust to experimental errors. In this work, we study the advantages of shallow randomized measurements over non-entangling single-qubit measurements for learning properties of quantum states. Although shallow measurements have shown advantages in selected applications, their usefulness across different learning tasks has not been systematically understood. Here, we develop a theoretical framework based on Clifford ensembles that incorporates shallow measurements into derandomized measurements, multi-shot protocols, common randomized measurements, error-mitigated estimators, and hybrid quantum-classical learning. Finally, we validate these results on IBM quantum hardware in experiments with up to 40 qubits and 46 layers of two-qubit gates. These results indicate that shallow-depth measurements can provide practical benefits on noisy quantum devices.