Embedding Matrices in Programmable Photonic Networks with Flexible Depth and Width
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914221494632448 |
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| author | Markowitz, Matthew Zelaya, Kevin Miri, Mohammad-Ali |
| author_facet | Markowitz, Matthew Zelaya, Kevin Miri, Mohammad-Ali |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_03696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embedding Matrices in Programmable Photonic Networks with Flexible Depth and Width Markowitz, Matthew Zelaya, Kevin Miri, Mohammad-Ali Optics 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. |
| title | Embedding Matrices in Programmable Photonic Networks with Flexible Depth and Width |
| topic | Optics |
| url | https://arxiv.org/abs/2503.03696 |