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The Aaronson–Ambainis conjecture
Show that every bounded low-degree polynomial on the Boolean cube with non-negligible variance has a variable of polynomially large influence.
| 1 | { |
| 2 | "domain": "physics-astronomy", |
| 3 | "topics": [ |
| 4 | "quantum-information", |
| 5 | "algorithms-complexity" |
| 6 | ], |
| 7 | "type": "proof", |
| 8 | "source": { |
| 9 | "key": "qiqcop", |
| 10 | "name": "QIQCOP Zoo", |
| 11 | "url": "https://qiqc-op.com/problem/op_a11fdfadc84e4379/", |
| 12 | "id": "op_a11fdfadc84e4379", |
| 13 | "curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo", |
| 14 | "poser": "Scott Aaronson and Andris Ambainis", |
| 15 | "status": "unsolved", |
| 16 | "as_of": "2026-10-20", |
| 17 | "catalog": "0521c19bbd38" |
| 18 | } |
| 19 | } |