pub fn YGate(radix: usize) -> UnitaryExpressionExpand description
The one-qudit Y gate. This is a Weyl-Heisenberg gate.
Defined as:
$$ Y = \omega^{(d-1)/2} X Z $$
where $\omega = e^{2\pi i / d}$, $X$ is the shift gate, and $Z$ is the clock gate. This choice of global phase is the natural qudit generalization of the Pauli Y gate: for $d = 2$ it reproduces
$$ Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} $$
In general the non-zero entry at row $(j+1 \bmod d)$, column $j$ is $\omega^{(d-1)/2} \cdot \omega^{j} = e^{2\pi i (2j + d - 1)/(2d)}$.