Embedding Matrices in Programmable Photonic Networks with Flexible Depth and Width

Abstract

We show that programmable photonic circuit architectures composed of alternating mixing layers and active layers offer a high degree of flexibility. This alternating configuration enables the systematic tailoring of both the network's depth (number of layers) and width (size of each layer) without compromising computational capabilities. From a mathematical perspective, our approach can be viewed as embedding an arbitrary target matrix into a higher-dimensional matrix, which can then be represented with fewer layers and larger active elements. We derive a general relation for the width and depth of a network that guarantees representing all $N\times N$ complex matrix operations. Remarkably, we show that just two such active layers, interleaved with passive mixing layers, are sufficient to universally implement arbitrary matrix transformations. This result promises a more adaptable and scalable route to photonic matrix processors.

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Cited by in corpus (1)

• Programmable Space-Frequency Linear Transformations in Photonic Interlacing Architectures