U3Gate

class U3Gate(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:

U3(\theta, \phi, \lambda) = RZ(\phi) RX(-\pi/2) RZ(\theta) RX(\pi/2) RZ(\lambda)

Circuit symbol:

     ┌───────────┐
q_0: ┤ U3(ϴ,φ,λ) ├
     └───────────┘

Matrix Representation:

\providecommand{\th}{\frac{\theta}{2}}\\\begin{split}U3(\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}

Examples:

U3(\theta, -\frac{\pi}{2}, \frac{\pi}{2}) = RX(\theta)

U3(\theta, 0, 0) = RY(\theta)

Create new U3 gate.

Methods Defined Here

U3Gate.control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Return a (multi-)controlled-U3 gate.

Parameters

num_ctrl_qubits (int) – number of control qubits.
label (str or None) – An optional label for the gate [Default: None]
ctrl_state (int or str or None) – control state expressed as integer, string (e.g. ‘110’), or None. If None, use all 1s.

Returns

controlled version of this gate.

Return type

ControlledGate

U3Gate.inverse()

Return inverted U3 gate.

$U3(\theta,\phi,\lambda)^{\dagger} =U3(-\theta,-\lambda,-\phi)$ )

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

Return definition in terms of other basic gates.

Get the duration.

Return instruction label

Return type

str

return instruction params.

Get the time unit of duration.

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