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

Abstract

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 a photon-loss threshold of ∼ 3.3 × 10 −3 which is about an order of magnitude higher than 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 ∼ 6.8 × 10 5 (1.4 × 10 7 ) which is significantly less by multiple orders of magnitude compared to other known linear optical schemes.