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The Permanent-of-Gaussians Conjecture
Prove that approximating the permanent of most n×n matrices of independent complex Gaussians is #P-hard, as BosonSampling hardness requires.
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| 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_af68b033a88ef934/", | |
| 12 | + "id": "op_af68b033a88ef934", | |
| 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 Alex Arkhipov", | |
| 15 | + "status": "unsolved", | |
| 16 | + "as_of": "2026-10-20", | |
| 17 | + "catalog": "0521c19bbd38" | |
| 18 | + } | |
| 19 | +} | |