Training saturation in layerwise quantum approximate optimization

Quantum Approximate Optimisation (QAOA) is the most studied gate based variational quantum algorithm today. We train QAOA one layer at a time to maximize overlap with an $n$ qubit target state. Doing so we discovered that such training always saturates -- called \textit{training saturation} some depth $p^*$, meaning past certain depth, can not be improved by adding subsequent layers. formulate necessary conditions for saturation. Numerically, find layerwise reaches its maximum $p^*=n$. The addition of coherent dephasing errors removes saturation, recovering robustness training. This study sheds new light on performance limitations and prospects QAOA.