Current proposals for scalable photonic quantum technologies require on-demand sources of indistinguishable single photons with very high efficiency (having unheralded loss below $1%$). Even with recent progress in the field there is still a significant gap between the requirements and state of the art performance. Here, we propose an on-chip source of multiplexed, heralded photons. Using quantum feedback control on a photon storage cavity with an optimized driving protocol, we estimate an on-demand efficiency of $99%$ and unheralded loss of order $1%$, assuming high efficiency detectors and intrinsic cavity quality factors of order $10^8$. We further explain how temporal- and frequency-multiplexing can be used in parallel to significantly reduce device requirements if single photon frequency conversion is possible with efficiency in the same range of $99%$.
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