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Resource-Optimal Programmable Photonics for Neural Networks

Ryan Hamerly, Jasvith Raj Basani, Alexander Sludds, Sri Krishna Vadlamani, Dirk Englund

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We study phase-shifter efficiency in programmable photonics, deriving an information-theoretic lower bound for phase shift in universal circuits, and proposing a “3-MZI” mesh that saturates this bound and requires 10× less phase than conventional designs.
DOI
10.1364/cleo_si.2025.ss184_1

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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 ≪2π. We derive a universal information-theoretic limit to the phase-shift efficiency of universal multiport interferometers and, based on a modified Mach–Zehnder Interferometer (MZI) design, propose a “3-MZI” architecture that approaches this limit to within a factor of 2×, approximately a 10× reduction in average phase shift over the prior art, where the average phase shift scales inversely with system size N as O(1/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 ≲0.2 radians without loss of accuracy.
The scalability of many programmable photonic circuits is limited by the 2π2π2π 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 ≪2π\ll 2π≪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 2×2\times2×, approximately a 10×10\times10× reduction in average phase shift over the prior art, where the average phase shift scales inversely with system size as O(1/N)O(1/\sqrt{N})O(1/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 ≲0.2\lesssim 0.2≲0.2 radians without loss of accuracy.
In recent years, there has been growing interest in analog information processing and unconventional computing using Photonic Integrated Circuits (PICs) to address the increasing demands of next-generation computing. This has driven the development of on-chip architectures capable of implementing fundamental linear operations such as matrix-vector multiplication (MVM), which plays a central role in fields such as quantum information processing and the acceleration of deep neural networks. Within the feed-forward paradigm, interleaved meshes of Mach–Zehnder Interferometers (MZIs) have emerged as the leading architecture for programmable integrated photonics (PIP), enabling real-time implementation of arbitrary linear transformations using tunable phase shifter elements. More recently, an alternative class of programmable photonic architectures based on Multi-Plane Light Conversion (MPLC) has been proposed, consisting of alternating diagonal phase-shifter layers and multimode mixing elements. Although these architectures lack a deterministic synthesis algorithm for the phase actuators, they have been shown to offer several advantages over conventional MZI-based architectures. In this thesis we investigate the properties and universal capabilities of MPLC architectures utilizing unequally spaced coupled waveguide arrays (CWAs), with a particular emphasis on the well-known Jx-lattice. Defect tolerance and self-calibration properties are studied, demonstrating substantially greater robustness to imperfections than conventional MZI meshes. We further introduce several extensions of the MPLC architecture that demonstrate its flexibility, such as the redistribution of amplitude modulators and their interchangeable use with phase shifters to realize universal transformations with a near-minimal number of tunable units. Collectively, these results provide a broader understanding of the capabilities of MPLC architectures and establish a foundation for their application as a flexible alternative and complement to MZI-based designs.