A Self-Similar Sine-Cosine Fractal Architecture for Multiport Interferometers

Integrated photonic architectures based on beamsplitter meshes have recently captured attention as a platform to accelerate many conventional computing tasks. Among these tasks, one that is fundamental to linear algebra and neural networks is matrix processing. We propose a novel architecture for multiport interferometric meshes based on the Sine-Cosine Fractal (SCF) decomposition of unitary matrices to implement arbitrary linear matrix transforms. The design we propose is unique in that it is self-similar, thus enabling the construction of large-scale modular multi-chiplet devices. We find that this modularity dictates the distribution of phase-shifts in the SCF mesh, due to which our design enjoys improved resilience to hardware imperfections as compared to conventional multiport interferometers. Additionally, the structure of this circuit enables systematic truncation, which is key in reducing the hardware footprint of the device, as well as training time for use in optical neural networks. Via numerical simulations, we show that truncated meshes maintain robust performance even under large fabrication errors, which is commensurate with present-day digital electronic deep neural network accelerators. This design is a step forward in the construction of large-scale programmable photonics, opening up prospects of scaling to practical machine learning and quantum computing applications.