Hu Hong-Ye, Gu Andi, Majumder Swarnadeep, Ren Hang, Zhang Yipei, Wang Derek S, You Yi-Zhuang, Minev Zlatko, Yelin Susanne F, Seif Alireza
Department of Physics, Harvard University, Cambridge, MA, USA.
IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA.
Nat Commun. 2025 Mar 26;16(1):2943. doi: 10.1038/s41467-025-57349-w.
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.
从量子系统中高效提取信息对于量子信息处理至关重要。经典影子能够通过少量测量来预测任意量子态的许多性质。虽然随机单比特测量在实验上易于实现且适用于学习低权重泡利可观测量，但对于非局域可观测量，它们的表现不佳。在测量前引入一个浅随机量子电路可提高高权重泡利可观测量和低秩性质的采样效率。然而，在实际中，这些电路可能存在噪声并使测量结果产生偏差。在此，我们提出了稳健浅影子方法，该方法在后期处理中采用贝叶斯推理来学习和减轻噪声。我们分析了噪声对采样复杂度和最优电路深度的影响。我们为在广泛的噪声过程下减轻误差的成功提供了理论保证。在超导量子处理器上的实验验证证实了我们的方法在预测诸如保真度和纠缠熵等各种态性质方面，即使存在实际噪声，相对于单比特测量也具有优势。因此，我们的协议为近期量子设备上的量子态表征提供了一种可扩展、稳健且采样高效的方法。
