发表机构
The University of Hong Kong; HK Institute of Quantum Science & Technology; Freie Universität Berlin; Dahlem Center for Complex Quantum Systems, Freie Universität Berlin; Helmholtz-Zentrum Berlin für Materialien und Energie（香港大学; 香港量子科学研究所; 柏林自由大学; 柏林自由大学达勒姆复杂量子系统中心; 柏林亥姆霍兹材料与能源中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明，在费米子线性光学中重现随机矩阵统计需要广泛的非高斯资源，其代价由单体缺陷ν量化，并与采样统计和制备资源定量关联。
AI 中文摘要
基于采样的量子优势提出了一个基本的资源问题：需要多少非高斯性才能重现通常与量子混沌相关的随机矩阵统计？被动费米子线性光学保持高斯结构，即使是哈尔随机模式混合也无法对斯莱特输入实现反集中。我们证明，克服这一障碍需要广泛的输入资源。对于任何纯半填充输入态，单体缺陷ν（定义为自然轨道占据方差的总和）必须随系统尺寸线性扩展。对于4N模式上有界大小块的乘积，该条件也是充分的，归一化碰撞矩渐近为2N/ν，而波特-托马斯值为2。对于四模式乘积，当缺陷密度趋于其最大值时，完整的波特-托马斯矩层级被精确恢复。假设平均情况下的硬度，近似经典采样在接近最大密度时仍然困难，误差容限随密度增加。双副本数涨落直接测量ν，且相同的量在确定性精确制备中下界非高斯资源模式和宇称保持局部门的总代价。因此，费米子随机性带有广泛的魔法代价，在采样统计、制备资源和实验可访问的见证之间建立了定量联系。
英文摘要
Sampling-based quantum advantage raises a basic resource question: how much non-Gaussianity is needed to reproduce the random-matrix statistics often associated with quantum chaos? Passive fermionic linear optics preserves Gaussian structure, and even Haar-random mode mixing fails to anticoncentrate for Slater inputs. We show that overcoming this obstruction requires an extensive input resource. For any pure half-filled input state, the one-body defect $ν$, defined as the summed occupation variance of the natural orbitals, must scale linearly with system size. For products of bounded-size blocks on $4N$ modes, this condition is also sufficient, with normalized collision moment asymptotic to $2N/ν$, compared with the Porter-Thomas value 2. For four-mode products, the full Porter-Thomas moment hierarchy is recovered precisely when the defect density tends to its maximum. Assuming average-case hardness, approximate classical sampling remains hard near maximal density, with an error tolerance that increases with the density. Two-copy number fluctuations measure $ν$ directly, and the same quantity lower-bounds the combined cost of non-Gaussian resource modes and parity-preserving local gates in deterministic exact preparation. Fermionic randomness therefore carries an extensive magic cost, with a quantitative link between sampling statistics, preparation resources, and an experimentally accessible witness.
Comments30 pages, 5 figures
