# Robustness of quantum algorithms against coherent control errors

arXiv: https://arxiv.org/abs/2303.00618 · HTML: https://mlsanity.com/paper/2303.00618/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2023.

## Built on by (most cited first, 4 of 4)

- [Training robust and generalizable quantum models](https://mlsanity.com/paper/2311.11871/) (2023)
- [A Comparative Analysis of Adversarial Robustness for Quantum and Classical Machine Learning Models](https://mlsanity.com/paper/2404.16154/) (2024)
- [A unifying framework for differentially private quantum algorithms](https://mlsanity.com/paper/2307.04733/) (2023)
- [The interplay of robustness and generalization in quantum machine learning](https://mlsanity.com/paper/2506.08455/) (2025)

## Abstract (arXiv)

Coherent control errors, for which ideal Hamiltonians are perturbed by unknown multiplicative noise terms, are a major obstacle for reliable quantum computing. In this paper, we present a framework for analyzing the robustness of quantum algorithms against coherent control errors using Lipschitz bounds. We derive worst-case fidelity bounds which show that the resilience against coherent control errors is mainly influenced by the norms of the Hamiltonians generating the individual gates. These bounds are explicitly computable even for large circuits, and they can be used to guarantee fault-tolerance via threshold theorems. Moreover, we apply our theoretical framework to derive a novel guideline for robust quantum algorithm design and transpilation, which amounts to reducing the norms of the Hamiltonians. Using the 3-qubit Quantum Fourier Transform as an example application, we demonstrate that this guideline targets robustness more effectively than existing ones based on circuit depth or gate count. Furthermore, we apply our framework to study the effect of parameter regularization in variational quantum algorithms. The practicality of the theoretical results is demonstrated via implementations in simulation and on a quantum computer.