Abstract
Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. We here introduce a fault-tolerant hybrid quantum computation by taking the advantages of both discrete variable (DV) and continuous variable (CV) systems. Particularly, we define a CV-DV hybrid qubit with bosonic cat-code and single photon, which is implementable in current photonic platforms. By the cat-code encoded in the CV part, the dominant loss errors are readily correctable without multi-qubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error correction code such as topological codes, exploring their potential merits in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource-efficient over all previous proposals in photon