McKay decomposer

The McKay decomposer (McKayDecomposer) is a single-qubit gate decomposer.

It decomposes any single-qubit unitary \(U\) into a sequence of (at most 5) single-qubit gates, consisting of Rz and Rx rotations:

\[U = R_z(\theta) \cdot R_x(\pi/2) \cdot R_z(\phi) \cdot R_x(\pi/2) \cdot R_z(\lambda). \]

The algorithm used by the McKay decomposer is described in McKay et al. (2017).

Global phase difference

Note that the resulting decomposition using the McKay decomposer (McKayDecomposer) is equal to the original gate, up to a (possible) difference in global phase. A difference in global phase can, in certain cases, lead to a semantically different circuit, therefore we urge the user to be aware of this risk.

Example decompositions of notable single-qubit gates are:

Unitary	Decomposition
I	\(I\)
H	\(Rz(\pi/2) \cdot X^{1/2} \cdot Rz(\pi/2)\)
X	\(X^{1/2} \cdot X^{1/2}\)
Y	\(X^{1/2} \cdot X^{1/2} \cdot Rz(\pi)\)
Z	\(Rz(\pi)\)
S	\(Rz(\pi/2)\)
T	\(Rz(\pi/4)\)