Robust quantum algorithms using Lipschitz bounds

Noise poses a major obstacle in current quantum devices. The literature contains various approaches for handling noise such as quantum error correction (QEC) or quantum error mitigation (QEM). These approaches have in common that they improve robustness of a given quantum circuit via additional steps, e.g., adding additional circuit elements to detect and compensate errors (QEC) or post-processing to filter out the effect of noise (QEM). However, there is no systematic framework for considering robustness w.r.t. noise already in the algorithm design as an explicit objective. The goal of this project is to use Lipschitz bounds, which are a well-established robustness measure in automatic control, to study the robustness of quantum algorithms w.r.t. noise.