Laser interferometry as a robust neuromorphic platform for machine learning

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 methods 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.

💡 Research Summary

The paper proposes a purely linear‑optical architecture for implementing neural networks, using only field displacements and interferometry applied to coherent states of light. Non‑linearity, essential for learning, is introduced not through optical non‑linear media but by encoding the input data directly into phase‑shift operations. Because the phase‑shift matrix contains trigonometric functions of the encoded angles, the measured quadrature expectation values become nonlinear functions of the inputs while the underlying optical circuit remains linear.

The authors adopt the Gaussian continuous‑variable (CV) formalism, describing an M‑mode system by its mean vector r and covariance matrix Σ. Linear optical elements—phase shifters R(ϕ), beamsplitters B(θ), and displacements D(α)—are represented by symplectic matrices, allowing straightforward simulation of the entire network by propagating only the first moments. The network architecture consists of a fully connected M×M interferometer where every pair of modes is linked by a tunable beamsplitter with transmissivity angle θ. Biases are implemented as pre‑interferometer displacements. The output is taken as the expectation value of the Q‑quadrature measured by homodyne detection, providing a real‑valued scalar analogous to a classical neuron’s activation.

Training is performed in situ. For Gaussian circuits, the gradient of any observable with respect to a circuit parameter can be obtained exactly by a parameter‑shift rule: ∂⟨O⟩/∂θ = ½