  Variational Quantum Algorithms (VQAs) are often viewed as the best hope for
near-term quantum advantage. However, recent studies have shown that noise can
severely limit the trainability of VQAs, e.g., by exponentially flattening the
cost landscape and suppressing the magnitudes of cost gradients. Error
Mitigation (EM) shows promise in reducing the impact of noise on near-term
devices. Thus, it is natural to ask whether EM can improve the trainability of
VQAs. In this work, we first show that, for a broad class of EM strategies,
exponential cost concentration cannot be resolved without committing
exponential resources elsewhere. This class of strategies includes as special
cases Zero Noise Extrapolation, Virtual Distillation, Probabilistic Error
Cancellation, and Clifford Data Regression. Second, we perform analytical and
numerical analysis of these EM protocols, and we find that some of them (e.g.,
Virtual Distillation) can make it harder to resolve cost function values
compared to running no EM at all. As a positive result, we do find numerical
evidence that Clifford Data Regression (CDR) can aid the training process in
certain settings where cost concentration is not too severe. Our results show
that care should be taken in applying EM protocols as they can either worsen or
not improve trainability. On the other hand, our positive results for CDR
highlight the possibility of engineering error mitigation methods to improve
trainability.
