Methodology for quantum logic gate construction

We present a general method to construct fault-tolerant quantum logic gates with a simple primitive, which is an analog of quantum teleportation. The technique extends previous results based on traditional quantum teleportation [Gottesman and Chuang, Nature (London) 402, 390 (1999)] and leads to straightforward and systematic construction of many fault-tolerant encoded operations, including the $\pi /8\mathrm{}$ and Toffoli gates. The technique can also be applied to the construction of remote quantum operations that cannot be directly performed.