We propose an all-linear-optical scheme to ballistically generate a cluster state for measurement-based topological fault-tolerant quantum computation using hybrid photonic qubits entangled in a continuous-discrete domain. Availability of near-deterministic Bell-state measurements on hybrid qubits is exploited for this purpose. In the presence of photon losses, we show that our scheme leads to a significant enhancement in both tolerable photon-loss rate and resource overheads. We report a photon-loss threshold higher than those of known optical schemes under a reasonable error model. Furthermore, the resource overhead is estimated to be significantly less by multiple orders of magnitude compared to other reported values in the literature.

https://link.aps.org/doi/10.1103/PhysRevLett.125.060501