UGate

class UGate(theta, phi, lam, label=None)

Bases: qiskit.circuit.gate.Gate

Generic single-qubit rotation gate with 3 Euler angles.

Implemented using two X90 pulses on IBM Quantum systems:

\[U(\theta, \phi, \lambda) = RZ(\phi - \pi/2) RX(\pi/2) RZ(\pi - \theta) RX(\pi/2) RZ(\lambda - \pi/2)\]

Circuit symbol:

     ┌──────────┐
q_0: ┤ U(ϴ,φ,λ) ├
     └──────────┘

Matrix Representation:

\[ \begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}U(\theta, \phi, \lambda) = \begin{pmatrix} \cos(\th) & -e^{i\lambda}\sin(\th) \\ e^{i\phi}\sin(\th) & e^{i(\phi+\lambda)}\cos(\th) \end{pmatrix}\end{split}\end{aligned}\end{align} \]

Examples:

\[U\left(\theta, -\frac{\pi}{2}, \frac{\pi}{2}\right) = RX(\theta)\]

\[U(\theta, 0, 0) = RY(\theta)\]

Create new U gate.

Methods Defined Here

control	Return a (multi-)controlled-U gate.
inverse	Return inverted U gate.

Attributes

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates.

duration

Get the duration.

label

Return instruction label

Return type

str

params

return instruction params.

unit

Get the time unit of duration.