  We propose a teleportation-based scheme to implement a universal set of
quantum gates with a four-component cat code, assisted by appropriate entangled
resource states and photon number resolving detection. The four-component cat
code features the ability to recover from single photon loss. Here, we propose
a concrete procedure to correct the single photon loss, including detecting the
single photon loss event and recovering the initial states. By concatenating
with standard qubit error correcting codes, we estimate the loss threshold for
fault-tolerant quantum computation and obtain a significant improvement over
the two-component cat code.
