Demonstration of robust and efficient quantum property learning with shallow shadows

Hong-Ye Hu, Andi Gu, Swarnadeep Majumder, Hang Ren, Yipei Zhang, Derek S. Wang, Yi-Zhuang You (), Zlatko Minev (), Susanne F. Yelin () and Alireza Seif ()
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Hong-Ye Hu: Harvard University
Andi Gu: Harvard University
Swarnadeep Majumder: IBM T.J. Watson Research Center
Hang Ren: Berkeley Center for Quantum Information and Computation
Yipei Zhang: Berkeley Center for Quantum Information and Computation
Derek S. Wang: IBM T.J. Watson Research Center
Yi-Zhuang You: University of California San Diego
Zlatko Minev: IBM T.J. Watson Research Center
Susanne F. Yelin: Harvard University
Alireza Seif: IBM T.J. Watson Research Center

Nature Communications, 2025, vol. 16, issue 1, 1-14

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

Date: 2025
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DOI: 10.1038/s41467-025-57349-w

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