In this talk, I plan to introduce our two recent works (arXiv: 2201.00752, arXiv: 2207.01403). I will begin with briefly introducing the basic concepts of quantum error mitigation (QEM) in the era of noisy intermediate-scale quantum (NISQ) devices and a typical QEM approach, namely the quasi-probability decomposition method. I will then make comments on this method from two aspects, i.e. its powerlessness on correlated noise and the physical meaning of its sampling cost, respectively. In the remaining time, I will focus on these two issues. In our first work (arXiv: 2201.00752), we use matrix product operators (MPO) to represent the noise channel to characterize and mitigate correlated noise in quantum circuits. As for the second work (arXiv:2207.01403), we find that the physical implementability, which is the sampling cost of implementing the noise inverse, is a good characterization of the decoherence effects.