Sub-quadratic scalable approximate linear converter using multi-plane light conversion with low-entropy mode mixers

Abstract

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 $O(N^2)$ phase shifters for exact synthesis of $N\times N$ matrices, limiting 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 uses low-entropy mode mixers, allowing more compact implementations compared to conventional mixers. We introduce Shannon matrix entropy as a measure of mode coupling strength in mixers and demonstrate that low-entropy mixers can preserve computational accuracy while reducing the requirements for the mixers. The approximation quality is evaluated using the maximum norm between the target and realized matrices. Numerical results show that the proposed method achieves sub-quadratic scaling of phase shifters by tolerating predefined error thresholds. To identify efficient architectures for implementing general linear matrices, we compare block-encoding (BE) and singular-value decomposition (SVD) schemes for realizing general linear matrices using unitary converters based on MPLC. Results indicate that BE exhibits superior iterative configuration properties beyond the unitary group. By characterizing the trade-offs between matrix entropy, number of phase shifter layers, and the error tolerance, this study provides a framework for designing scalable and efficient approximate optical converters.

References in corpus (33)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Deep Learning with Coherent Nanophotonic Circuits
• Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation
• Parallel convolution processing using an integrated photonic tensor core
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Laguerre-Gaussian mode sorter
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• All Optical Neural Network with Nonlinear Activation Functions
• Efficient and mode selective spatial mode multiplexer based on Multi-Plane Light Conversion
• Programmable unitary spatial modes manipulation
• Measurement-induced quantum criticality under continuous monitoring
• Single chip photonic deep neural network with accelerated training
• Photonic tensor cores for machine learning
• Design of optical neural networks with component imprecisions
• Limit Theorem for Continuous-Time Quantum Walk on the Line
• Free-space optical neural network based on thermal atomic nonlinearity
• Robust architecture for programmable universal unitaries
• Random unistochastic matrices
• Unitary stochastic matrix ensembles and spectral statistics
• Universal Linear Intensity Transformations Using Spatially-Incoherent Diffractive Processors
• Birkhoff's polytope and unistochastic matrices, N=3 and N=4
• Scalable and Robust Photonic Integrated Unitary Converter
• Exact Elliptic Compactons in Generalized Korteweg-DeVries Equations
• Spectral correlations of individual quantum graphs
• BitNet: Scaling 1-bit Transformers for Large Language Models
• Auto-calibrating Universal Programmable Photonic Circuits: Hardware Error-Correction and Defect Resilience
• The Goldilocks Principle of Learning Unitaries by Interlacing Fixed Operators with Programmable Phase Shifters on a Photonic Chip
• Large-Scale Crosstalk-Corrected Thermo-Optic Phase Shifter Arrays in Silicon Photonics
• Lower-depth programmable linear optical processors
• Fast reconstruction of programmable integrated interferometers
• Saturation of entropy production in quantum many-body systems
• Low-depth, compact and error-tolerant photonic matrix-vector multiplication beyond the unitary group
• Dynamic Sparse Training of Diagonally Sparse Networks