  Extracting useful information from noisy near-term quantum simulations
requires error mitigation strategies. A broad class of these strategies rely on
precise characterization of the noise source. We study the robustness of
probabilistic error cancellation and tensor network error mitigation when the
noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the
existence of a threshold in the robustness of these error mitigation methods
for random spatially local circuits in spatial dimensions $D \geq 2$: noise
characterization disorder below the threshold rate allows for error mitigation
up to times that scale with the number of qubits. For one-dimensional circuits,
by contrast, mitigation fails at an $\mathcal{O}(1)$ time for any imperfection
in the characterization of disorder. As a result, error mitigation is only a
practical method for sufficiently well-characterized noise. We discuss further
implications for tests of quantum computational advantage, fault-tolerant
probes of measurement-induced phase transitions, and quantum algorithms in
near-term devices.
