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In recent years, miniaturization and integration of photonic microwave oscillators by optical frequency division approach have witnessed rapid progress. In this work, we report on-chip low phase noise photonic microwave generation based on a planar chip design. Dual lasers are co-locked to a silicon nitride spiral resonator and their relative phase noise is measured below the cavity thermal noise limit, resulting in record low on-chip relative optical phase noise. A broadband integrated electro-optic comb up to 3.43 THz (27 nm) bandwidth is utilized to divide down the relative phase noise of the spiral resonator referenced lasers to the microwave domain. All-around record-low phase noise is achieved for planar chip-based photonic microwave oscillators from 10 Hz to 10 kHz offsets. The planar chip design, high technology-readiness level, foundry-ready processing, combined with the exceptional phase noise performance for our work represent a major advance of integrated photonic microwave oscillators.

A computer's clock rate ultimately determines the minimum time between sequential operations or instructions. Despite exponential advances in electronic computer performance owing to Moore's Law and increasingly parallel system architectures, computer clock rates have remained stagnant at $\sim5~\mathrm{GHz}$ for almost two decades. This poses an intractable problem for applications requiring real-time processing or control of ultrafast information systems. Here we break this barrier by proposing and experimentally demonstrating computing based on an end-to-end and all-optical recurrent neural network harnessing the ultrafast nature of linear and nonlinear optical operations while avoiding electronic operations. The all-optical computer realizes linear operations, nonlinear functions, and memory entirely in the optical domain with $>100~\mathrm{GHz}$ clock rates. We experimentally demonstrate a prototypical task of noisy waveform classification as well as perform ultrafast in-situ analysis of the soliton states from integrated optical microresonators. We further illustrate the application of the architecture for generative artificial intelligence based on quantum fluctuations to generate images even in the absence of input optical signals. Our results highlight the potential of all-optical computing beyond what can be achieved with digital electronics by utilizing ultrafast linear, nonlinear, and memory functions and quantum fluctuations.