The paper presents a robust shallow shadows protocol for efficient and accurate quantum state characterization. This protocol uses Bayesian inference to learn and mitigate noise in classical shadow tomography, a technique that leverages randomized measurements to estimate various properties of quantum states. The authors address the limitations of traditional methods, such as the poor performance of random single-qubit measurements for nonlocal observables and the high sample complexity required for predicting low-rank observables. By prepending a shallow random quantum circuit to the measurements, the protocol maintains experimental feasibility while improving sample complexity for a broader class of observables, including high-weight Paulis and global low-rank properties like fidelity. The robust shallow shadows protocol is theoretically analyzed to understand its performance under different noise models, particularly single-qubit depolarizing noise. The analysis shows that noise reduces the optimal circuit depth but increases the sample complexity. The authors also develop a tensor network-based postprocessing technique to efficiently represent and mitigate the effects of noise, ensuring unbiased and accurate predictions. Experimental results on a superconducting quantum processor demonstrate the effectiveness of the protocol. The protocol accurately recovers state properties such as fidelity, entanglement entropy, and subsystem purity for various application states, including the plus state and a cluster state. The protocol shows improved sample complexity compared to random single-qubit measurements, especially for high-weight Pauli observables. Additionally, the protocol is applied to the AKLT resource state, a non-stabilizer state, to predict subsystem purities, further validating its robustness and efficiency. The robust shallow shadows protocol offers a scalable, robust, and sample-efficient approach for characterizing quantum states, with potential applications in quantum machine learning, quantum chemistry, and quantum many-body physics.The paper presents a robust shallow shadows protocol for efficient and accurate quantum state characterization. This protocol uses Bayesian inference to learn and mitigate noise in classical shadow tomography, a technique that leverages randomized measurements to estimate various properties of quantum states. The authors address the limitations of traditional methods, such as the poor performance of random single-qubit measurements for nonlocal observables and the high sample complexity required for predicting low-rank observables. By prepending a shallow random quantum circuit to the measurements, the protocol maintains experimental feasibility while improving sample complexity for a broader class of observables, including high-weight Paulis and global low-rank properties like fidelity. The robust shallow shadows protocol is theoretically analyzed to understand its performance under different noise models, particularly single-qubit depolarizing noise. The analysis shows that noise reduces the optimal circuit depth but increases the sample complexity. The authors also develop a tensor network-based postprocessing technique to efficiently represent and mitigate the effects of noise, ensuring unbiased and accurate predictions. Experimental results on a superconducting quantum processor demonstrate the effectiveness of the protocol. The protocol accurately recovers state properties such as fidelity, entanglement entropy, and subsystem purity for various application states, including the plus state and a cluster state. The protocol shows improved sample complexity compared to random single-qubit measurements, especially for high-weight Pauli observables. Additionally, the protocol is applied to the AKLT resource state, a non-stabilizer state, to predict subsystem purities, further validating its robustness and efficiency. The robust shallow shadows protocol offers a scalable, robust, and sample-efficient approach for characterizing quantum states, with potential applications in quantum machine learning, quantum chemistry, and quantum many-body physics.