Towards the Information-Theoretic Limit of Programmable Photonics

The scalability of many programmable photonic circuits is limited by the $2π$ tuning range needed for the constituent phase shifters. To address this problem, we introduce the concept of a phase-efficient circuit architecture, where the average phase shift is $\ll 2π$. We derive a universal information-theoretic limit to the phase-shift efficiency of universal multiport interferometers, and propose a "3-MZI" architecture that approaches this limit to within a factor of $2\times$, approximately a $10\times$ reduction in average phase shift over the prior art, where the average phase shift scales inversely with system size as $O(1/\sqrt{N})$. For non-unitary circuits, we show that the 3-MZI saturates the theoretical bound for Gaussian-distributed target matrices. Using this architecture, we show optical neural network training with all phase shifters constrained to $\lesssim 0.2$ radians without loss of accuracy.