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Variational Quantum Algorithms (VQAs) are widely viewed as the best hope fornear-term quantum advantage. However, recent studies have shown that noise canseverely limit the trainability of VQAs, e.g., by exponentially flattening thecost landscape and suppressing the magnitudes of cost gradients. ErrorMitigation (EM) shows promise in reducing the impact of noise on near-termdevices. Thus, it is natural to ask whether EM can improve the trainability ofVQAs. In this work, we first show that, for a broad class of EM strategies,exponential cost concentration cannot be resolved without committingexponential resources elsewhere. This class of strategies includes as specialcases Zero Noise Extrapolation, Virtual Distillation, Probabilistic ErrorCancellation, and Clifford Data Regression. Second, we perform analytical andnumerical analysis of these EM protocols, and we find that some of them (e.g.,Virtual Distillation) can make it harder to resolve cost function valuescompared to running no EM at all. As a positive result, we do find numericalevidence that Clifford Data Regression (CDR) can aid the training process incertain settings where cost concentration is not too severe. Our results showthat care should be taken in applying EM protocols as they can either worsen ornot improve trainability. On the other hand, our positive results for CDRhighlight the possibility of engineering error mitigation methods to improvetrainability.

Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?