Resource-Efficient Topological Fault-Tolerant 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 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. More specifically, we report a photon-loss threshold of ∼3.3×10^{-3}, which is higher than those of known optical schemes under a reasonable error model. Furthermore, resource overheads to achieve logical error rate of 10^{-6}(10^{-15}) is estimated to be ∼8.5×10^{5}(1.7×10^{7}), which is significantly less by multiple orders of magnitude compared to other reported values in the literature.