## Building Toffoli gates from 1-gates and CNOT

Fix a number $n$ of qubits. In this post, we show how to build the Toffoli gates $T^{|k\rangle}_{|l\rangle}$ out of 1-gates and the CNOT gate. When combined with this post, we conclude that the set of 1-gates together with CNOT form a universal set of quantum gates. Since $T^{|k\rangle}_{|l\rangle}$ is built from the Pauli gate…