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Optical computing with integrated photonics brings a pivotal paradigm shiftto data-intensive computing technologies. However, the scaling of on-chipphotonic architectures using spatially distributed schemes faces the challengeimposed by the fundamental limit of integration density. Synthetic dimensionsof light offer the opportunity to extend the length of operand vectors within asingle photonic component. Here, we show that large-scale, complex-valuedmatrix-vector multiplications on synthetic frequency lattices can be performedusing an ultra-efficient, silicon-based nanophotonic cavity acousto-opticmodulator. By harnessing the resonantly enhanced strong electro-optomechanicalcoupling, we achieve, in a single such modulator, the full-range phase-coherentfrequency conversions across the entire synthetic lattice, which constitute afully connected linear computing layer. Our demonstrations open up the routetowards the experimental realizations of frequency-domain integrated opticalcomputing systems simultaneously featuring very large-scale data processing andsmall device footprints.

Scaling optical computing in synthetic frequency dimension using integrated cavity acousto-optics