We present a method for implementing an optical neural network using only linear optical resources, namely field displacement and interferometry applied to coherent states of light. The nonlinearity required for learning in a neural network is realized via an encoding of the input into phase shifts allowing for far more straightforward experimental implementation compared to previous proposals for, and demonstrations of, $\textit{in situ}$ inference. Beyond $\textit{in situ}$ inference, the method enables $\textit{in situ}$ training by utilizing established techniques like parameter shift rules or physical backpropagation to extract gradients directly from measurements of the linear optical circuit. We also investigate the effect of photon losses and find the model to be very resilient to these.

翻译：我们提出了一种仅使用线性光学资源（即场位移和干涉测量）实现光学神经网络的方法，并将其应用于相干光态。神经网络学习所需的非线性通过将输入编码为相位偏移来实现，与先前提出的以及演示的$\textit{原位}$推理方案相比，该方法允许实验实现更为直接。除了$\textit{原位}$推理外，该方法通过利用已建立的技术（如参数偏移规则或物理反向传播）直接从线性光学电路的测量中提取梯度，从而实现了$\textit{原位}$训练。我们还研究了光子损耗的影响，发现该模型对此具有极强的鲁棒性。