Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons

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 building on 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 us 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 superconducting and trapped-ion systems, which allows us to find various efficient routes towards fault-tolerant quantum computing.