  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.
