  We propose an efficient protocol to fully reconstruct a set of high-fidelity
quantum gates. Usually, the efficiency of reconstructing high-fidelity quantum
gates is limited by the sampling noise. Our protocol is based on a perturbative
approach and has two stages. In the first stage, the initial part of noisy
quantum gates is reconstructed by measuring traces of maps, and the trace can
be measured by amplifying the noise in a way similar to randomised benchmarking
and quantum spectral tomography. In the second stage, by amplifying the
non-unital part using the unital part, we can efficiently reconstruct the
non-unital part. We show that the number of measurements needed in our protocol
scales logarithmically with the error rate of gates.
