  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 photonic platforms, allowing to achieve a record-high loss threshold among
existing CV and hybrid approaches. We discuss its realization not only in
all-photonic platforms but also in other hybrid platforms including
superconduting and trapped-ion systems, which allows us to find various
efficient routes towards fault-tolerant quantum computing.
