Methodology for quantum logic gate constructions

Abstract

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 {\bf 402}, 390, 1999) and leads to straightforward and systematic construction of many fault-tolerant encoded operations, including the $\pi/8$ and Toffoli gates. The technique can also be applied to the construction of remote quantum operations that cannot be directly performed.