Hybrid Rydberg atom plus SDP algorithm achieves 0.651-approximation for quantum Max Cut, improving on the prior 0.614 SDP-only bound and remaining effective at 89% ground-state fidelity.
Conjectured Bounds for 2-Local Hamiltonians via Token Graphs
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abstract
We explain how the maximum energy of the Quantum MaxCut, XY, and EPR Hamiltonians on a graph $G$ are related to the spectral radii of the token graphs of $G$. From numerical study, we conjecture new bounds for these spectral radii based on properties of $G$. We show how these conjectures tighten the analysis of existing algorithms, implying state-of-the-art approximation ratios for all three Hamiltonians. Our conjectures also provide simple combinatorial bounds on the ground state energy of the antiferromagnetic Heisenberg model, which we prove for bipartite graphs.
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2026 2verdicts
UNVERDICTED 2representative citing papers
Level-ℓ Kikuchi graphs of random 2r-uniform hypergraphs spectrally approximate those of the complete hypergraph at near-optimal sampling rates for r ≤ ℓ ≤ n/2.
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A 0.651-approximation to quantum Max Cut via Rydberg atoms
Hybrid Rydberg atom plus SDP algorithm achieves 0.651-approximation for quantum Max Cut, improving on the prior 0.614 SDP-only bound and remaining effective at 89% ground-state fidelity.
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Kikuchi Graphs of Random Hypergraphs are Approximately Johnson
Level-ℓ Kikuchi graphs of random 2r-uniform hypergraphs spectrally approximate those of the complete hypergraph at near-optimal sampling rates for r ≤ ℓ ≤ n/2.