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) RX(-\pi/2) RZ(\theta) RX(\pi/2) RZ(\lambda)

Equivalent simplified form:

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

Circuit symbol:

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

Matrix Representation:

\providecommand{\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}

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

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

Return a (multi-)controlled-U 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

inverse

UGate.inverse()

Return inverted U gate.

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

Attributes

condition_bits

Get Clbits in condition.

Return type

List[Clbit]

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

name

Return the name.

num_clbits

Return the number of clbits.

num_qubits

Return the number of qubits.

params

return instruction params.

unit

Get the time unit of duration.

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