Scalable photonic quantum computing architectures pose stringent requirements on photonic processing devices. The needs for low-loss high-speed reconfigurable circuits and near-deterministic resource state generators are some of the most challenging requirements. Here, we develop an integrated photonic platform based on thin-film lithium niobate and interface it with deterministic solid-state single-photon sources based on quantum dots in nanophotonic waveguides. The generated photons are processed with low-loss circuits programmable at speeds of several gigahertz. We realize a variety of key photonic quantum information processing functionalities with the high-speed circuits, including on-chip quantum interference, photon demultiplexing, and reprogrammability of a four-mode universal photonic circuit. These results show a promising path forward for scalable photonic quantum technologies by merging integrated photonics with solid-state deterministic photon sources in a heterogeneous approach to scaling up.