  We propose a scalable architecture for a quantum network based on a simple
on-chip photonic circuit that performs loss-tolerant two-qubit measurements.
The circuit consists of two quantum emitters positioned in the arms of an
on-chip Mach-Zehnder interferometer composed of waveguides with chiral
light--matter interfaces. The efficient chiral light--matter interaction allows
the emitters to perform high-fidelity intranode two-qubit parity measurements
within a single chip, and to emit photons to generate internode entanglement,
without any need for reconfiguration. We show that by connecting multiple
circuits of this kind into a quantum network, it is possible to perform
universal quantum computation with heralded two-qubit gate fidelities ${\cal F}
\sim 0.998$ achievable in state-of-the-art quantum dot systems.
