Quantum error mitigation with classical shadows

Mitigating errors in quantum information processing devices is especially important in the absence of fault-tolerance. An effective method in suppressing state preparation error is using multiple copies to distill the ideal component from a noisy quantum state. Here, we use classical shadows and randomized measurement to circumvent the need for coherent access to multiple copies at an exponential cost. We extensively study the scaling of resources using numerical simulations and find that the overhead is still favorable compared to full state tomography. We also apply our method to an experiment with trapped ions and successfully improve the fidelity of preparing a GHZ state. The analysis of the improved data also reveals the nature of errors affecting the experiment. Hence, our results provide a directly applicable method for mitigating errors in near-term quantum computers.