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	+}