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Zero noise extrapolation is one of the simplest error mitigation techniques and, in many practical situations, it can be applied with a relatively small sampling cost. The main advantage of ZNE is that the technique can be applied without a detailed knowledge of the undelying noise model. Therefore it can be a good option in situations where tomography is impractical.
In some instances the results of the extrapolation can exhibit a large bias
{cite}Mari_2021_PRA
. ZNE may not be helpful in cases where a low degree
polynomial curve obtained by fitting the noisy expectation values does not match the
zero-noise limit. When using circuits of less trivial depth on real devices, the
lowest error points may be too noisy for the extrapolation to show improvement over
the unmitigated result {cite}Lowe_2021_PRR
.
For a simple example in which the application of ZNE reduces the estimation error when compared to the unmitigated result, see: