Resource-Efficient Topological Fault-Tolerant Quantum Computation with Hybrid Entanglement of Light
S. Omkar, Yong Siah Teo, Hyunseok Jeong
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 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 $\ensuremath{\sim}3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which is higher than those of known optical schemes under a reasonable error model. Furthermore, resource overheads to achieve logical error rate of ${10}^{\ensuremath{-}6}({10}^{\ensuremath{-}15})$ is estimated to be $\ensuremath{\sim}8.5\ifmmode\times\else\texttimes\fi{}{10}^{5}(1.7\ifmmode\times\else\texttimes\fi{}{10}^{7})$, which is significantly less by multiple orders of magnitude compared to other reported values in the literature.