Optical nonlinearity plays a pivotal role in quantum information processing using photons, from heralded single-photon sources to long-sought quantum repeaters. Despite the availability of strong light-atom interaction, an all-optical nonlinearity is highly desired for more scalable quantum protocols. Here, we realize quantum nanophotonic integrated circuits in thin-film InGaP with a record-high second-order optical nonlinearity of $1.5%$---the ratio of the single-photon trimodal coupling strength ($g/2pi=11.2$ MHz) and cavity-photon loss rate. We demonstrate photon-pair generation via degenerate spontaneous parametric down conversion in the InGaP photonic circuit with an ultrahigh rate exceeding 27.5 MHz per 1 $mu$W pump power and large coincidence-to-accidental ratio up to $1.4times 10^4$. Our work shows InGaP as a potentially transcending platform for quantum nonlinear optics and quantum information applications.
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