Optical Arbitrary Vector‐Matrix Multiplication in a Single Time‐Varying Ring

Optical computing is increasingly seen as a promising route to fast machine learning by utilizing the ultrafast speed of light and its intrinsic parallelism. A recent challenge is to obtain a scalable and programmable vector‐matrix multiplication module with compact integrated photonic technology. Here, we propose an architecture based on a time‐varying optical ring to realize arbitrary vector‐matrix multiplication with spatial complexity and evolution time. The non‐Hermitian synthetic frequency lattice is built where we prove its universality, and further confirming its scalability with high precision and full programmability remaining. We also highlight the strong expressivity within a fixed physical footprint by demonstrating no intrinsically hard‐to‐learn matrix in our architecture. Our proposal is naturally suitable for chip‐scale realization by overcoming the limitation from spatial complexity in conventional optical computing, which paves the way toward integrated, large‐scale, and scalable photonic computing systems.