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arXiv · 2607.00945

The Dynamical Lie Algebra of QAOA-MaxCut on the Complete Graph

Jonathan Allcock·Pei Yuan·Shengyu Zhang
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Abstract

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.

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Jonathan Allcock, Pei Yuan, Shengyu Zhang. 2026-07-01. The Dynamical Lie Algebra of QAOA-MaxCut on the Complete Graph. https://arxiv.org/abs/2607.00945

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