Towards the Information-Theoretic Limit of Programmable Photonics

TL;DR

This paper introduces a new phase-efficient architecture for programmable photonic circuits that significantly reduces the average phase shift needed, approaching theoretical limits and enabling scalable optical neural network training.

Contribution

The paper proposes a universal information-theoretic limit for phase-shift efficiency and introduces the 3-MZI architecture that approaches this limit, reducing phase shifts by about ten times compared to prior designs.

Findings

The 3-MZI architecture approaches the theoretical phase-shift efficiency limit.

Average phase shift scales as O(1/√N), enabling larger systems.

Optical neural networks can be trained with phase shifters constrained to ~0.2 radians without accuracy loss.

Abstract

The scalability of many programmable photonic circuits is limited by the $2\pi$ 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 $\ll 2\pi$. 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.