  Variational quantum algorithms are tailored to perform within the constraints
of current quantum devices, yet they are limited by performance-degrading
errors. In this study, we consider a noise model that reflects realistic gate
errors inherent to variational quantum algorithms. We investigate the
decoherence of a variationally prepared quantum state due to this noise model,
which causes a deviation from the energy estimation in the variational
approach. By performing a perturbative analysis of optimized circuits, we
determine the noise threshold at which the criteria set by the stability lemma
is met. We assess our findings against the variational quantum approximate
optimization algorithm for $3$-SAT problem instances and unstructured search
with up to $10$ qubits and $30$ layers. Moreover, we show that certain gate
errors have a significantly smaller impact on the coherence of the state,
allowing us to reduce the execution time without compromising performance.

Quantum Physics