Training Saturation in Layerwise Quantum Approximate Optimisation
This addresses performance limitations in QAOA, a key quantum algorithm, but is incremental as it focuses on a specific training issue.
The study tackled the problem of training saturation in layerwise Quantum Approximate Optimisation (QAOA), finding that overlap with a target state saturates at a depth p*=n, and that adding coherent dephasing errors removes this saturation.
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} -- at some depth $p^*$, meaning that past a certain depth, overlap can not be improved by adding subsequent layers. We formulate necessary conditions for saturation. Numerically, we find layerwise QAOA reaches its maximum overlap at depth $p^*=n$. The addition of coherent dephasing errors to training removes saturation, recovering robustness to layerwise training. This study sheds new light on the performance limitations and prospects of QAOA.