Training Saturation in Layerwise Quantum Approximate Optimisation

TL;DR

This paper investigates the phenomenon of training saturation in layerwise Quantum Approximate Optimization (QAOA), revealing that beyond a certain depth, additional layers do not improve overlap, but this saturation can be mitigated by dephasing errors.

Contribution

It introduces the concept of training saturation in layerwise QAOA, formulates necessary conditions for saturation, and shows how dephasing errors can remove saturation, enhancing robustness.

Findings

Training saturation occurs at depth p* = n.

Adding dephasing errors removes saturation.

Layerwise QAOA reaches maximum overlap at depth p* = n.

Abstract

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.