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Aluminum gallium arsenide-on-insulator (AlGaAsOI) exhibits large $\chi^\left(2\right)$ and $\chi^\left(3\right)$ optical nonlinearities, a wide tunable bandgap, low waveguide propagation loss, and a large thermo-optic coefficient, making it an exciting platform for integrated quantum photonics. With ultrabright sources of quantum light established in AlGaAsOI, the next step is to develop the critical building blocks for chip-scale quantum photonic circuits. Here we expand the quantum photonic toolbox for AlGaAsOI by demonstrating edge couplers, 3-dB splitters, tunable interferometers, and waveguide crossings with performance comparable to or exceeding silicon and silicon-nitride quantum photonic platforms. As a demonstration, we demultiplex photonic qubits through an unbalanced interferometer, paving the route toward ultra-efficient and high-rate chip-scale demonstrations of photonic quantum computation and information applications.