Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

TL;DR

This paper investigates whether error mitigation techniques can enhance the trainability of noisy variational quantum algorithms, revealing that many strategies do not resolve noise issues efficiently, but some, like Clifford Data Regression, show promise under specific conditions.

Contribution

The study provides a comprehensive analysis of various error mitigation strategies, demonstrating their limitations and potential benefits for improving VQA trainability.

Findings

Exponential cost concentration cannot be resolved without exponential resources for many EM strategies.

Some EM methods, like Virtual Distillation, can hinder cost function resolution.

Clifford Data Regression can aid training when noise impact is moderate.

Abstract

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.