Provable Classical and Quantum Local Algorithms for Max- k-Cut and Quantum Advantage at Moderate Girth

arXiv:2609.39042 · quant-ph, cs.DS, math.OC · Submitted 2026-09-30 · Read on arXiv

quant-ph, cs.DS, math.OC

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Quantum Approximate Optimization Algorithm — 4× in this paper
• Anti-correlation — 2× in this paper · explained in 3 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Combinatorial Optimization — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adjacency Matrix — 1× in this paper · explained in 1 episode
• Degeneracy — 1× in this paper · explained in 3 episodes
• Hypergraph — 1× in this paper · explained in 2 episodes
• Semidefinite Programming (SDP) — 1× in this paper · explained in 3 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• Local algorithms for Maximum Cut and Minimum Bisection on locally treelike regular graphs of large degree
• Quantum Approximate Optimization of Integer Graph Problems and Surpassing Semidefinite Programming for Max-k-Cut
• Limitations of Local Quantum Algorithms on Random Max-k-XOR and Beyond
• The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: A Typical Case
• A Quantum Approximate Optimization Algorithm
• Lower bounding the MaxCut of high girth 3-regular graphs using the QAOA
• A proof of Alon's second eigenvalue conjecture and related problems
• A Classical Algorithm Which Also Beats $\frac{1}{2}+\frac{2}{\pi}\frac{1}{\sqrt{D}}$ For High Girth MAX-CUT
• Large Cuts with Local Algorithms on Triangle-Free Graphs
• Optimization of the Sherrington-Kirkpatrick Hamiltonian
• Optimization on Sparse Random Hypergraphs and Spin Glasses

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