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Growing interest in quantum computing for practical applications has led to a surge in the availability of programmable machines for executing quantum algorithms1,2. Present-day photonic quantum computers3–7 have been limited either to non-deterministic operation, low photon numbers and rates, or fixed random gate sequences. Here we introduce a full-stack hardware−software system for executing many-photon quantum circuit operations using integrated nanophotonics: a programmable chip, operating at room temperature and interfaced with a fully automated control system. The system enables remote users to execute quantum algorithms that require up to eight modes of strongly squeezed vacuum initialized as two-mode squeezed states in single temporal modes, a fully general and programmable four-mode interferometer, and photon number-resolving readout on all outputs. Detection of multi-photon events with photon numbers and rates exceeding any previous programmable quantum optical demonstration is made possible by strong squeezing and high sampling rates. We verify the non-classicality of the device output, and use the platform to carry out proof-of-principle demonstrations of three quantum algorithms: Gaussian boson sampling, molecular vibronic spectra and graph similarity8. These demonstrations validate the platform as a launchpad for scaling photonic technologies for quantum information processing. A system for realizing many-photon quantum circuits is presented, comprising a programmable nanophotonic chip operating at room temperature, interfaced with a fully automated control system.