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

• URL: http://arxiv.org/abs/2607.00945v1
• Date: Wed, 01 Jul 2026 13:45:02 GMT
• Title: The Dynamical Lie Algebra of QAOA-MaxCut on the Complete Graph
• Abstract summary: We show that the variance of the associated loss function scales linearly in the number of qubits.<n>This solves an open problem from [ASYZ26] and confirms that such systems do not exhibit barren plateaus.
• Score: 9.937940252962443
• License: http://creativecommons.org/licenses/by/4.0/
• 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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