Synthesis of unitaries with Clifford+T circuits

Implementing a unitary operation using a universal gate set is a fundamental problem in quantum computing. The problem naturally arises when we want to implement some quantum algorithm on a fault tolerant quantum computer. Most fault tolerant protocols allow one to implement only Clifford circuits (those generated by CNOT, Hadamard and Phase gates). To achieve universal quantum computation one needs to add at least one non-Clifford gate. One of the common examples is