Laser interferometry as a robust neuromorphic platform for machine learning

TL;DR

This work demonstrates a linear-optical neural network built from laser interferometry and field displacements that achieves nonlinear learning by encoding inputs into phase shifts within a Gaussian continuous-variable framework. The approach enables in situ training via parameter-shift gradients or adjoint backpropagation, while remaining robust to photon loss and avoiding reliance on optical nonlinearities. Numerical experiments across nonlinear regression and both binary and multilabel classification show high accuracy and resilience, with practical insight into gradient estimation trade-offs and hardware-feasibility. The results highlight the practicality of integrated photonics for neuromorphic computing and point to future avenues for quantum enhancements and architectural extensions.

Abstract

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.

Figures (15)

• Figure 1: Schematic diagram of linear optical circuit for nonlinear processing with an input $\vec{x} = [x_1,x_2,...,x_M]^T \in \mathbb{R}^M$. The nonlinearity is realized by encoding the input into quadrature phase shifts $\mathbf R(x)$ while affine transformations are carried out using an $M \times M$ interferometer $\mathbf U(\vec{\theta})$ and displacements $d(\alpha)$ with the model output being extracted using homodyne measurements of the $Q$ quadrature. Note that $\vec{\theta}$ denotes the set of transmittivity angles for the $M(M-1)/2$ beamsplitters that comprise the interferometer.
• Figure 2: Regression results with Gaussian CV neural network. We set the standard deviation of the Gaussian noise to $\sigma=0.05$. The noisy training data are shown as red circles. The output prediction for test set values of $x$ are shown as blue crosses.
• Figure 3: Effect of photon loss after each layer of the optical circuit when fitting on noisy data from the function $f(x)=x^3$. The heatmap on the right shows the magnitude $|\alpha|$ of the displacements applied to each mode at each layer of the optical circuit.
• Figure 4: Training data used for binary classification problems. We set the standard deviation of the Gaussian noise to $\sigma=0.05$.
• Figure 5: Classification results with ONN on the test set. The red data points correspond to class 1 and the blue correspond to class 0. The heatmap on the left shows the probability predicted by the network that a point in a particular region belongs to class 1 along with points from the test set. The confusion matrix for the test set is shown on the right.