Resource-efficient and fault-tolerant topological quantum computation with hybrid entanglement of light.

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 the 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. More specifically, we report threshold photon-loss rate of $\sim3.36\times 10^{-3}$ which is about an order of magnitude higher than many optical schemes for fault tolerant quantum computation. Furthermore, resource overheads to achieve logical error rate of $10^{-6}(10^{-15})$ is estimated to be $\sim6.78\times10^{5}(1.44\times10^{7})$ which is significantly less by multiple orders of magnitude compared to other known linear optical schemes.