Sub-quadratic scalable approximate linear converter using multi-plane light conversion with low-entropy mode mixers
Yoshitaka Taguchi
Optical computing is emerging as a promising platform for energy-efficient, high-throughput hardware in deep learning. A key challenge lies in the realization of optical matrix–vector multiplication, which often requires O ( N 2 ) modulators for the exact synthesis of N × N matrices, limiting its scalability. In this study, we propose an approximate matrix realization method using multi-plane light conversion (MPLC) that reduces both the system size and the number of phase shifters while maintaining acceptable error bounds. This approach introduces low-entropy mode mixers, in which couplings between optical modes are weak. We demonstrate that such mixers can preserve computational accuracy while reducing hardware requirements, enabling more flexible and compact implementations in unitary converters using MPLC. We further investigate converters with fewer phase-shifter layers than the theoretical minimum and show that they function as approximate converters by tolerating predefined error thresholds, achieving sub-quadratic scaling. To identify efficient architectures for implementing general linear matrices using unitary converters, we compare block-encoding (BE) and singular-value decomposition (SVD) schemes. Results indicate that BE exhibits superior iterative configuration properties. By characterizing the trade-offs between entropy of mode mixers, number of phase shifters, and error tolerance, this study provides a framework for designing scalable and efficient approximate optical converters. Finally, using model quantization techniques, we demonstrate that the proposed method reduces the number of required phase shifters by half while preserving the accuracy of a text classification model, highlighting the effectiveness of error-tolerant model training for analog computing platforms.
arXiv:2412.11515•Journal of the Optical Society of America B•Aug 20, 2025•2 citations