Photonic systolic array for all-optical matrix-matrix multiplication

TL;DR

This paper introduces a fully optical photonic systolic array for matrix-matrix multiplication, enabling high-density, efficient AI computations without electronic bottlenecks, verified through numerical simulations.

Contribution

It presents the first all-optical photonic systolic array design for matrix multiplication, utilizing homodyne detection and adjoint-based optical module design.

Findings

Achieves a theoretical computation density of 6.2 PMACs/mm²/s.

Numerically verifies operation of a 4x4 array.

Enables optical-only matrix multiplication for AI workloads.

Abstract

Systolic arrays have proven to be highly efficient for parallelized matrix-matrix multiplication (MMM), utilizing synchronized, heartbeat-like data flows across an array of processing elements. While optical structures such as waveguide crossbar arrays and Mach-Zehnder interferometer-based meshes serve as photonic equivalents to the systolic arrays, the disparity between the two input matrices for multiplication -- one using optical signals and the other with system-defined parameters -- gives rise to a bottleneck in modern machine-learning tasks, such as evaluating attention scores in large language models. Here, we propose a photonic systolic array that performs MMM entirely with optical signals, utilizing homodyne detection at each array cell. Adjoint-based design of compact on-chip freeform optical modules enables precise control of light flow without bulky waveguide coupling schemes. The operation of a $4\times4$ photonic systolic array is numerically verified, achieving a theoretical computation density of $6.2~\mathrm{PMACs}/\mathrm{mm}^2/\mathrm{s}$. This design marks a significant step toward practical photonic computing hardware for modern AI workloads.