Realistic quantum photonic neural networks

Quantum photonic neural networks are variational photonic circuits that can be trained to implement high-fidelity quantum operations. However, work-to-date has assumed idealized components, including a perfect $\pi$ Kerr nonlinearity. Here, we investigate the limitations of realistic quantum photonic neural networks that suffer from fabrication imperfections leading to photon loss and imperfect routing, and weak nonlinearities, showing that they can learn to overcome most of these errors. Using the example of a Bell-state analyzer, we demonstrate that there is an optimal network size, which balances imperfections versus the ability to compensate for lacking nonlinearities. With a sub-optimal $\pi/10$ effective Kerr nonlinearity, we show that a network fabricated with current state-of-the-art processes can achieve an unconditional fidelity of 0.891, that increases to 0.999999 if it is possible to precondition success on the detection of a photon in each logical photonic qubit. Our results provide a guide to the construction of viable, brain-inspired quantum photonic devices for emerging quantum technologies.