# What would be a complete QC circuit?

In classical computing NAND is a complete set (functionally complete) of binary operations, namely any Boolean circuit can be expressed using NAND gates.

Is there an equivalent for quantum computing circuit? It should be possible imho to have such a complete set because any rotation ob Bloch sphere is reducible to Euler angles based rotation matrices: $R=X(\alpha)Y(\beta)Z(\gamma)$.

• Wouldn't this imply that $U = H \otimes \mathrm{TOFFOLI}$ is an example of a single unitary operator which is (approximately) universal for quantum computation? One could similarly consider $U' = T \otimes H \otimes \mathrm{CNOT}$. – Niel de Beaudrap Jan 24 '18 at 19:31