Predicting many state properties with robust shallow circuit shadow tomography

Efficient prediction of many quantum state properties is crucial for quantum information processing. Through the use of randomized measurements and shallow circuits, classical shadow tomography emerges as a highly efficient, promising approach compatible with near-term quantum processors. This work presents the Robust Shallow Shadow (RSS) method, designed to operate effectively mitigate correlated noise, and provides a theoretical analysis of RSS behavior within the shallow-circuit region. We further illustrate the efficacy of RSS by demonstrating its performance using superconducting quantum processors.