u#
Single-qubit SU(2) gate.
The SU(2) matrix in the computational basis is parametrized using Euler angles:
\[\begin{split}U(\theta, \phi, \lambda) =
\begin{pmatrix}
cos(\theta / 2) & -e^{i\lambda}\sin{\theta/2} \\
e^{i\phi}\sin{\theta/2} & e^{i(\lambda+\phi)}\cos{\theta/2}
\end{pmatrix}\end{split}\]
where the angles \(\theta\), \(\phi\) and \(\lambda\) are in radians. They are the angles of subsequent Z, Y and Z Euler rotations:
\[U(\theta, \phi, \lambda) = R_Z(\phi) \: R_Y(\theta) \: R_Z(\lambda)\]
It rotates the qubit state around an arbitrary axis on the Bloch sphere.
Some common single-qubit gates expressed as U gates:
\[\begin{split}X = U(\pi, -\pi/2, \pi/2)\\
Y = U(\pi, 0, 0)\\
Z = U(0, 0, \pi)\\
H = U(\pi / 2, 0, \pi)\\
S = U(0, \pi / 4, \pi / 4)\\
T = U(0, \pi / 8, \pi / 8)\end{split}\]
References
https://openqasm.com/language/gates.html#built-in-gates
Full path: iqm.pulse.gates.u
Functions
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Unitary for an SU(2) gate. |
Classes
SU(2) gate implemented using PRX. |
Inheritance
