Papers › Local classical MAX-CUT algorithm outperforms p=2 QAOA on high-girth regular graphs
Local classical MAX-CUT algorithm outperforms p=2 QAOA on high-girth regular graphs
Kunal Marwaha
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The p-stage Quantum Approximate Optimization Algorithm (QAOAₚ) is a promising approach for combinatorial optimization on noisy intermediate-scale quantum (NISQ) devices, but its theoretical behavior is not well understood beyond p=1. We analyze QAOA₂ for the maximum cut problem (MAX-CUT), deriving a graph-size-independent expression for the expected cut fraction on any D-regular graph of girth > 5 (i.e. without triangles, squares, or pentagons). We show that for all degrees D ≥2 and every D-regular graph G of girth > 5, QAOA₂ has a larger expected cut fraction than QAOA₁ on G. However, we also show that there exists a $2$-local randomized classical algorithm A such that A has a larger expected cut fraction than QAOA₂ on all G. This supports our conjecture that for every constant p, there exists a local classical MAX-CUT algorithm that performs as well as QAOAₚ on all graphs.
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