Simultaneous multiply-accumulate operations in optical computing by Jacobi time-wave packets

The increasing computational demands of artificial intelligence strain the speed and energy efficiency of electronic processors, particularly for multiply-accumulate (MAC) operations. Current photonic approaches face limitations in scalability and power consumption. Here we demonstrate that multiplexing orthogonal time-wave packets based on Jacobi polynomials enables simultaneous execution of multiple MAC operations within a single clock cycle. Experimentally, this method achieves real-time unscrambling of 2 GBd 6x6 MIMO signals and nonlinear optical vector processing for XOR and XNOR logic gates across multiple 10 GBd wavelength channels. This approach reduces processing steps and hardware complexity, offering a scalable and energy-efficient pathway for optical computing in large-scale neural networks. Our findings suggest that Jacobi polynomial time multiplexing can enhance the performance and integration density of photonic processors for AI applications.