When should I use PEC?#
The main advantage of PEC is that, under the assumption of perfect gate tomography, it provides an unbiased estimation of expectation values. This means that, in the limit of many samples, the error mitigated expectation values converge to the ideal expectation values.
PEC is a noise-aware technique that converges to the ideal noiseless results only if we have the full tomographic knowledge of the hardware gates. Indeed, in order to represent ideal gates as linear combination of noisy gates, one typically needs to know the super-operator matrix associated to each noisy gate.
Another practical problem of PEC is that it involves the execution of many different circuits. This typically requires more clock time compared to the repeated execution of equal circuits. Batched execution of circuits, if supported by the hardware provider, can alleviate this problem to some extent.