A sharp interaction-degree threshold for simulating QAOA
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913153327038464 |
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| author | Āboliņš, Ralfs Ambainis, Andris |
| author_facet | Āboliņš, Ralfs Ambainis, Andris |
| contents | We identify a sharp interaction-degree threshold for the classical simulation of QAOA with $2$-local cost functions. At degree $3$, classical sampling from depth-$1$ QAOA with small multiplicative error would collapse the polynomial hierarchy to its third level. At degree $2$, exact classical sampling from depth-$p$ QAOA on $n$ qubits runs in time $n^{O(1)}$ whenever $p = O(\log n)$. The hard degree-$3$ instances have trivially optimizable cost functions, so sampling hardness does not by itself imply a quantum optimization advantage. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22758 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A sharp interaction-degree threshold for simulating QAOA Āboliņš, Ralfs Ambainis, Andris Quantum Physics Computational Complexity We identify a sharp interaction-degree threshold for the classical simulation of QAOA with $2$-local cost functions. At degree $3$, classical sampling from depth-$1$ QAOA with small multiplicative error would collapse the polynomial hierarchy to its third level. At degree $2$, exact classical sampling from depth-$p$ QAOA on $n$ qubits runs in time $n^{O(1)}$ whenever $p = O(\log n)$. The hard degree-$3$ instances have trivially optimizable cost functions, so sampling hardness does not by itself imply a quantum optimization advantage. |
| title | A sharp interaction-degree threshold for simulating QAOA |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2605.22758 |