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

Jasvith Raj Basani, Sri Krishna Vadlamani, Saumil Bandyopadhyay, Dirk Englund, Ryan Hamerly

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We propose a novel architecture for multiport interferometers based on the Sine-Cosine fractal decomposition of unitary matrices. Our design is modular, resilient to hardware imperfections and enables systematically truncated for use in optical neural networks.
DOI
10.1364/cleo_at.2023.jw2a.87

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Multiport interferometers based on integrated beamsplitter meshes have recently captured interest as a platform for many emerging technologies. In this paper, we present a novel architecture for multiport interferometers based on the Sine-Cosine fractal decomposition of a unitary matrix. Our architecture is unique in that it is self-similar, enabling the construction of modular multi-chiplet devices. Due to this modularity, our design enjoys improved resilience to hardware imperfections as compared to conventional multiport interferometers. Additionally, the structure of our circuit enables systematic truncation, which is key in reducing the hardware footprint of the chip as well as compute time in training optical neural networks, while maintaining full connectivity. Numerical simulations show that truncation of these meshes gives robust performance even under large fabrication errors. This design is a step forward in the construction of large-scale programmable photonics, removing a major hurdle in scaling up to practical machine learning and quantum computing applications.
Multiport interferometers based on integrated beamsplitter meshes are widely used in photonic technologies. While the rectangular mesh is favored for its compactness and uniformity, its geometry resists conventional self-configuration approaches, which are essential to programming large meshes in the presence of fabrication error. Here, we present a configuration algorithm, related to the $2\ifmmode\times\else\texttimes\fi{}2$ block decomposition of a unitary matrix, that overcomes this limitation. Our proposed algorithm is robust to errors, requires no prior knowledge of the process variations, and relies only on external sources and detectors. We show that self-configuration using this technique reduces the effect of fabrication errors by the same quadratic factor observed in triangular meshes. This relaxes a significant limit to the size of multiport interferometers, removing a major roadblock to the scaling of optical quantum and machine-learning hardware.
Universal multiport interferometers (UMIs) have emerged as a key tool for performing arbitrary linear transformations on optical modes, enabling precise control over the state of light in essential applications of classical and quantum information processing such as neural networks and boson sampling. While UMI architectures based on Mach–Zehnder interferometer networks are well established, alternative approaches that involve interleaving fixed multichannel mixing layers and phase masks have recently gained interest due to their high robustness to losses and fabrication errors. However, these approaches currently lack optimal analytical methods to compute design parameters with a low optical depth. In this work, we introduce a constructive decomposition of unitary matrices using a sequence of 2 N +5 phase masks interleaved with 2 N +4 discrete Fourier transform matrices. This decomposition can be leveraged to design universal interferometers based on phase masks and multimode interference couplers, implementing a discrete Fourier transform, offering an analytical alternative to conventional numerical-optimization-based designs and reducing by a factor of 3 the previous best-known analytical methods.