Classical Shadows With Noise

The classical shadows protocol, recently introduced by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)], is a quantum-classical protocol to estimate properties of an unknown quantum state. Unlike full state tomography, the can be implemented on near-term hardware requires few measurements make many predictions with high success probability. In this paper, we study effects noise protocol. particular, consider scenario in which circuits involved are subject various known channels derive analytical upper bound for sample complexity terms shadow seminorm both local global noise. Additionally, modifying post-processing step noiseless define new estimator that remains unbiased presence As applications, show our results used prove rigorous bounds cases depolarizing amplitude damping.