  Mitigating errors in quantum information processing devices is especially
important in the absence of fault tolerance. An effective method in suppressing
state-preparation errors is using multiple copies to distill the ideal
component from a noisy quantum state. Here, we use classical shadows and
randomized measurements to circumvent the need for coherent access to multiple
copies at an exponential cost. We study the scaling of resources using
numerical simulations and find that the overhead is still favorable compared to
full state tomography. We optimize measurement resources under realistic
experimental constraints and apply our method to an experiment preparing
Greenberger-Horne-Zeilinger (GHZ) state with trapped ions. In addition to
improving stabilizer measurements, the analysis of the improved results reveals
the nature of errors affecting the experiment. Hence, our results provide a
directly applicable method for mitigating errors in near-term quantum
computers.
