# Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

arXiv: https://arxiv.org/abs/2109.01051 · HTML: https://mlsanity.com/paper/2109.01051/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 102 references that are in the map.
- First posted on arXiv 2 Sep 2021.

## Builds on (most cited first, 11 of 11)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm](https://mlsanity.com/paper/1910.02071/) (2019)
- [Adaptive shot allocation for fast convergence in variational quantum algorithms](https://mlsanity.com/paper/2108.10434/) (2021)
- [Non-trivial symmetries in quantum landscapes and their resilience to quantum noise](https://mlsanity.com/paper/2011.08763/) (2020)
- [Long-time simulations with high fidelity on quantum hardware](https://mlsanity.com/paper/2102.04313/) (2021)

## Built on by (most cited first, 14 of 14)

- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Trainability barriers and opportunities in quantum generative modeling](https://mlsanity.com/paper/2305.02881/) (2023)
- [Subtleties in the trainability of quantum machine learning models](https://mlsanity.com/paper/2110.14753/) (2021)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [Thermodynamic AI and the fluctuation frontier](https://mlsanity.com/paper/2302.06584/) (2023)
- [Reduction of finite sampling noise in quantum neural networks](https://mlsanity.com/paper/2306.01639/) (2023)
- [Inference-Based Quantum Sensing](https://mlsanity.com/paper/2206.09919/) (2022)
- [Error Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis](https://mlsanity.com/paper/2209.11514/) (2022)
- [Quantum Natural Policy Gradients: Towards Sample-Efficient Reinforcement Learning](https://mlsanity.com/paper/2304.13571/) (2023)
- [Quantum-Classical Separations in Shallow-Circuit-Based Learning with and without Noises](https://mlsanity.com/paper/2405.00770/) (2024)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [Classical State Preparation for Variational Quantum Algorithms via Reinforcement Learning](https://mlsanity.com/paper/2605.23138/) (2026)

## Abstract (arXiv)

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.