Curator's Take
This article delivers the first closed‑form description of the dynamical Lie algebra underlying QAOA‑MaxCut on a fully connected graph and proves that the loss‑function variance grows linearly with qubit count, thereby ruling out barren plateaus for this setting. By settling an open problem from recent trainability studies, it strengthens the theoretical foundation for scaling variational algorithms on dense hardware graphs and suggests that QAOA can remain optimizable even as system size increases. The result is limited to complete‑graph instances, so extending the analysis to sparser or hardware‑native connectivity will be a crucial next step.
— Mark Eatherly
Summary
We give an analytical expression for the dynamical Lie algebra corresponding to the QAOA-MaxCut problem on complete graphs, and show that the variance of the associated loss function scales linearly in the number of qubits. This solves an open problem from [ASYZ26] and confirms that such systems do not exhibit barren plateaus. The proof is based on projecting the dynamical Lie algebra generators onto subspaces given by the Schur-Weyl duality between irreducible representations of the unitary and symmetric groups.