Experimental demonstration of the quantum advantage over classical simulations with Boson Sampling is currently under intensive investigation. There seems to be a scalability issue to the necessary number of bosons on the linear optical platforms and the experiments, such as the recent Boson Sampling with 20 photons on 60-port interferometer by H. Wang et al., Phys. Rev. Lett.123 (2019) 250503, are usually carried out on a small interferometer, much smaller than the size necessary for the no-collision regime. Before demonstration of quantum advantage, it is urgent to estimate exactly how the classical computations necessary for sampling from the output distribution of Boson Sampling are reduced when a smaller-size interferometer is used. This work supplies such a result, valid with arbitrarily close to 1 probability, which reduces in the no-collision regime to the previous estimate by Clifford and Clifford. One of the results with immediate application to current experiments with Boson Sampling is that classically sampling from the interference of [Formula: see text] single bosons on an [Formula: see text]-port interferometer is at least as hard as that with [Formula: see text] single bosons in the no-collision regime, i.e. on a much larger interferometer with at least [Formula: see text] ports.

中文翻译：

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从不可区分玻色子的量子干涉中采样的经典复杂性

与玻色子采样的经典模拟相比，量子优势的实验证明目前正在深入研究中。线性光学平台和实验上必要的玻色子数量似乎存在可扩展性问题，例如 H. Wang 等人最近在 60 端口干涉仪上使用 20 个光子进行的玻色子采样，Phys。Rev. Lett.123 (2019) 250503，通常在小型干涉仪上进行，远小于无碰撞机制所需的尺寸。在展示量子优势之前，迫切需要准确估计在使用较小尺寸的干涉仪时如何减少从玻色子采样的输出分布中采样所需的经典计算。这项工作提供了这样一个结果，以任意接近 1 的概率有效，这在无碰撞机制中减少到 Clifford 和 Clifford 先前的估计。立即应用于当前玻色子采样实验的结果之一是，经典地从 [公式：请参阅文本] 单个玻色子在 [公式：请参阅文本] 端口干涉仪的干扰中采样至少与 [公式：请参阅文本] 端口干涉仪一样难：见文本] 无碰撞状态下的单玻色子，即在一个更大的干涉仪上，至少有 [公式：见文本] 端口。