AI 中文总结
本研究在线性模式区域下，确立了带阈值和奇偶测量的玻色采样的典型输出概率估计的平均情况#P难度，证明其难处理结构在二元粗粒化下可保持，为相关量子优势实验提供理论支撑。
AI 中文摘要
玻色采样是展示量子优势的最具代表性候选方案之一。然而，尽管玻色采样的计算复杂度依赖于光子数分辨探测，但许多与实验相关的设置和应用却使用基于阈值或奇偶测量的二元读出，其计算复杂度尚未得到严格表征。在本研究中，我们调查了线性模式区域下带阈值和奇偶测量的玻色采样的计算复杂度，其中模式数量随光子数量线性缩放，且与当前实验最为相关。具体而言，我们确立了阈值和奇偶玻色采样中典型输出概率估计的平均情况#P难度，这是证明对应采样问题经典难度的关键要素。所得的不精确边界与线性模式区域下标准光子数分辨玻色采样的先前难度结果中获得的边界相匹配。关键技术要素是一种由相干分束器旋转诱导的傅里叶系数提取方法，该方法可从粗粒度输出概率中提取隐藏的难处理成分。这些结果表明，即使在碰撞主导的区域中，光子数分辨玻色采样的难处理输出概率结构也能在自然的二元粗粒化下保持。
英文摘要
BosonSampling is among the most prominent candidates for demonstrating quantum advantage. However, while the hardness of BosonSampling relies on photon-number-resolving detection, many experimentally relevant settings and applications instead use binary readout based on threshold or parity measurements, whose computational complexity has not yet been rigorously characterized. In this work, we investigate the computational complexity of BosonSampling with threshold and parity measurements in the linear-mode regime, where the number of modes scales linearly with the number of photons and is most relevant to current experiments. In particular, we establish average-case #P-hardness of estimating typical output probabilities in threshold and parity BosonSampling, a crucial ingredient in proving the classical hardness of the corresponding sampling problems. The resulting imprecision bounds match those obtained in prior hardness results for standard photon-number-resolving BosonSampling in the linear-mode regime. The key technical ingredient is a Fourier-coefficient extraction method, induced by coherent beam-splitter rotations, that extracts hidden hard components within coarse-grained output probabilities. These results indicate that the hard output-probability structure of photon-number-resolving BosonSampling can persist under natural binary coarse-grainings, even in collision-dominant regimes.
Comments60 pages, 5 figures
