Lower-depth programmable linear optical processors

Abstract

Programmable linear optical processors (LOPs) can have widespread applications in computing and information processing due to their capabilities to implement reconfigurable on-chip linear transformations. A conventional LOP that uses a mesh of Mach-Zehnder interferometers (MZIs) requires $2N+3$ stages of phase shifters for $N\times N$ matrices. However, it is beneficial to reduce the number of phase shifter stages to realize a more compact and lower-loss LOP, especially when long and lossy electro-optic phase shifters are used. In this work, we propose a novel structure for LOPs that can implement arbitrary matrices as long as they can be realized by previous MZI-based schemes. Through numerical analysis, we further show that the number of phase shifter stages in the proposed structure can be reduced to $N+2$ and $N+3$ for a large number of random dense matrices and sparse matrices, respectively. This work contributes to the realization of compact, low-loss, and energy-efficient programmable LOPs.

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• Low-depth, compact and error-tolerant photonic matrix-vector multiplication beyond the unitary group
• Photonic Circuit of Arbitrary Non-Unitary Systems
• Sub-quadratic scalable approximate linear converter using multi-plane light conversion with low-entropy mode mixers
• Universal low-depth two-unitary design of programmable photonic circuits
• Embedding Matrices in Programmable Photonic Networks with Flexible Depth and Width