玻色子采样实验中梯度的参数移位规则
Parameter-Shift Rules for Gradients in Boson Sampling Experiments
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中文总结 AI 辅助
研究在玻色子采样实验中计算福克玻色子采样跃迁概率梯度的方法，通过稳健光子损失模型推导\(n\)阶参数移位规则，证明该方法在特定条件下有效，且无法推广到高斯玻色子采样，通过与有限差分对比验证了方法的有效性。
中文摘要 AI 辅助
我们为光子量子实验使用稳健的光子损失模型，推导了用于计算向有损干涉仪发送\(n\)个光子时福克玻色子采样跃迁概率梯度的\(n\)阶参数移位规则。还表明一般无法将此梯度方法推广到高斯玻色子采样情况。仅在干涉仪传输矩阵可分解为对角损失矩阵与纯酉矩阵乘积的特定情形下，能得到由检测到的光子总数两倍给出的有限阶参数移位规则。通过与实际硬件上的有限差分比较性能，证明了所提方法的有效性。
英文摘要
Using a robust photon loss model for photonic quantum experiments, we derive $n-$th order parameter-shift rules for computing gradients of Fock boson sampling transition probabilities where $n$ photons are sent into a lossy interferometer. We also show that in general it is not possible to generalize this gradient recipe to the case of Gaussian boson sampling. Only in the specific case where the transmission matrix of the interferometer can be factorized as a diagonal loss matrix premultiplied by a pure unitary it is possible to obtain parameter-shift rules with a finite order given by twice the total number of photons detected. We demonstrate the efficacy of the proposed method by comparing its performance against finite differences on real hardware.
