  Graph codes play an important role in photonic quantum technologies as they
provide significant protection against qubit loss, a dominant noise mechanism.
Here, we develop methods to analyse and optimise measurement-based tolerance to
qubit loss and computational errors for arbitrary graph codes. Using these
tools we identify optimised codes with up to 12 qubits and asymptotically-large
modular constructions. The developed methods enable significant benefits for
various photonic quantum technologies, as we illustrate with novel all-photonic
quantum repeater states for quantum communication and high-threshold
fusion-based schemes for fault-tolerant quantum computing.
