We study the hardness of classically simulating boson sampling with superposition and Gaussian input states at nonzero photon indistinguishability. We find that, similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference terms in both these boson sampling variants. For superposition sampling, we find that it is not simulable with out method at zero indistinguishability, which is evidence for the computational hardness of this problem, and we find that it is simulable at any level of particle distinguishability, similar to regular boson sampling. If an efficient classical algorithm to approximate a given sum over permanents is found, this approach also leads to an efficient classical algorithm to simulate Gaussian boson sampling in the presence of distinguishability.

中文翻译：

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部分可区分的叠加和高斯玻色子采样的可模拟性

我们研究了在非零光子不可区分的情况下经典模拟玻色子采样与叠加和高斯输入状态的难度。我们发现，类似于常规的玻色子采样，可分辨性在这两个玻色子采样变体中引起多光子干扰项的指数衰减。对于叠加采样，我们发现在没有不可分辨性的情况下无法用无方法模拟，这证明了该问题的计算难度，并且我们发现，在任何级别的粒子可分辨性上，它都是可模拟的，类似于常规的玻色子采样。如果找到了一种有效的经典算法，可以近似于永久物上的给定总和，那么这种方法也会导致一种有效的经典算法，在存在可区分性的情况下模拟高斯玻色子采样。