u

Full path: iqm.pulse.gates.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:

\[\begin{split}X = U(\pi, -\pi/2, \pi/2)\\ Y = U(\pi, 0, 0)\\ Z = U(0, 0, \pi)\\ H = U(\pi / 2, 0, \pi)\\ S = U(0, \pi / 4, \pi / 4)\\ T = U(0, \pi / 8, \pi / 8) SH = C_XYZ = U(\pi / 2, 0, \pi /2)\\ HS^\dagger = C_{ZYX} = U(\pi / 2, \pi / 2, \pi)\\\end{split}\]

References

https://openqasm.com/language/gates.html#built-in-gates

Module Attributes

PI_2	Fundamental mathematical constant pi divided by two for performance.
CLIFFORDS_TO_EULER_DECOMPOSITION	Mapping of names used to describe Clifford gates to the tuples \(\theta, \phi, \lambda\) representing their ZYZ Euler angle decompositions.
ANGLE_THRESHOLD	If the angle is below this threshold, it is understood to be zero.

Functions

get_haar_random_unitary([d, rng])	Generates a random unitary matrix drawn uniformly from Haar measure.
get_su2_params(unitary[, threshold])	Calculate parameters for an SU(2) gate given its unitary.
get_unitary_u(theta, phi, lam)	Unitary for an SU(2) gate.

Classes

UGate

SU(2) gate implemented using PRX.

Inheritance