Efficient learning of Pauli channels: learning sparse models

The recent development of randomized compiling ensures that the general noise channel afflicting a universal quantum device can be reduced to stochastic Pauli noise. To characterize and optimize the remaining errors, methods are needed to characterize Pauli noise channels in intermediate and large-scale quantum devices. Here we introduce estimation protocols with relative error guarantees that enable efficient reconstructions of both complete and sparse Pauli channels. The protocol developed and analyzed is a variant of randomized benchmarking and the recently introduced cycle benchmarking. Like those protocols, the estimate is robust to state preparation and measurement error (SPAM). This robustness to SPAM together with the relative precision guarantees make the protocol appropriate for applications involving the characterization of high-accuracy gates. These results enable a host of applications beyond just characterizing noise in large-scale quantum systems: they pave the way to tailoring quantum codes, optimizing decoders, and customizing fault tolerance protocols to suit a particular device.