Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

Variational Quantum Algorithms (VQAs) are widely viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs by exponentially flattening the cost landscape. 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 noisy VQAs. In this work, we first unify many of the most widely studied EM protocols in the literature under one framework. Moreover, under this framework, we show that exponential cost concentration cannot be resolved without spending exponential resources. Second, we show analytically and numerically that, surprisingly, some EM protocols 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.