  Quantum error mitigation is a technique used to post-process errors occurring
in the quantum system, which reduces the expected errors and achieves higher
accuracy. One method of quantum error mitigation is zero-noise extrapolation,
which involves amplifying the noise and then extrapolating the observable
expectation of interest back to a noise-free point. This method usually relies
on the error model of the noise, as error rates for different levels of noise
are assumed during the noise amplification process. In this paper, we propose
that the purity of output states in noisy circuits can assist in the
extrapolation process, eliminating the need for assumptions about error rates.
We also introduce the quasi-polynomial model from the linearity of quantum
channel for extrapolation of experimental data, which can be reduced to other
proposed models. Furthermore, we verify our purity-assisted zero-noise
extrapolation by performing numerical simulations and experiments on the online
public quantum computation platform, Quafu, to compare it with the routine
zero-noise extrapolation and virtual distillation methods. Our results
demonstrate that this modified method can suppress the random fluctuation of
operator expectation measurement, and effectively reduces the bias in
extrapolation to a level lower than both the zero-noise extrapolation and
virtual distillation methods, especially when the error rate is moderate.
