Demonstration of robust and efficient quantum property learning with shallow shadows

• DOI: 10.1038/s41467-025-57349-w
• Publication Date: 2025-03-26T08:46:30Z
• Authors: Hong-Ye Hu; Andi Gu; Swarnadeep Majumder; Hang Ren; Yipei Zhang; Derek S. Wang; Yi-Zhuang You; Zlatko Minev; Susanne F. Yelin; Alireza Seif

Extracting information efficiently from quantum systems is crucial for processing. Classical shadows enable predicting many properties of arbitrary states using few measurements. While random single-qubit measurements are experimentally friendly and suitable learning low-weight Pauli observables, they perform poorly nonlocal observables. Introducing a shallow circuit before improves sample efficiency high-weight observables low-rank properties. However, in practice, these circuits can be noisy bias the measurement results. Here, we propose robust shadows, which employs Bayesian inference to learn mitigate noise postprocessing. We analyze effects on complexity optimal depth. provide theoretical guarantees success error mitigation under wide class processes. Experimental validation superconducting processor confirms advantage our method, even presence realistic noise, over diverse state properties, such as fidelity entanglement entropy. Our protocol thus offers scalable, robust, sample-efficient method characterization near-term devices. Fast reliable characterisation key part technologies development. authors demonstrate way embed classical shadow estimation enabling an efficient extract systems.