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Mitigating errors in quantum information processing devices is especiallyimportant in the absence of fault tolerance. An effective method in suppressingstate-preparation errors is using multiple copies to distill the idealcomponent from a noisy quantum state. Here, we use classical shadows andrandomized measurements to circumvent the need for coherent access to multiplecopies at an exponential cost. We study the scaling of resources usingnumerical simulations and find that the overhead is still favorable compared tofull state tomography. We optimize measurement resources under realisticexperimental constraints and apply our method to an experiment preparingGreenberger-Horne-Zeilinger (GHZ) state with trapped ions. In addition toimproving stabilizer measurements, the analysis of the improved results revealsthe nature of errors affecting the experiment. Hence, our results provide adirectly applicable method for mitigating errors in near-term quantumcomputers.

Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors