  Zero-noise extrapolation provides an especially useful error mitigation
method for noisy intermediate-scale quantum devices. Our analysis, based on
matrix product density operators, of the transverse-field Ising model with
depolarizing noise, reveals both advantages and inherent problems associated
with zero-noise extrapolation when simulating non-equilibrium many-body
dynamics. On the one hand, interestingly, noise alters systematically the
behavior of the Loschmidt echo at the dynamical phase transition times,
doubling the number of non-analytic points, and hence inducing an error that,
inherently, cannot be mitigated. On the other, zero-noise extrapolation may be
employed to recover quantum revivals of the Loschmidt echo, which would be
completely missed in the absence of mitigation, and to retrieve faithfully
noise-free inter-site correlations. Our results, which are in good agreement
with those obtained using quantum simulators, reveal the potential of matrix
product density operators for the investigation of the performance of quantum
devices with a large number of qubits and deep noisy quantum circuits.
