U2Gate

class qiskit.circuit.library.U2Gate(phi, lam, label=None)

Bases: Gate

Single-qubit rotation about the X+Z axis.

Implemented using one X90 pulse on IBM Quantum systems:

Warning

This gate is deprecated. Instead, the following replacements should be used

U2(\phi, \lambda) = U\left(\frac{\pi}{2}, \phi, \lambda\right)

circuit = QuantumCircuit(1)
circuit.u(pi/2, phi, lambda)

Circuit symbol:

     ┌─────────┐
q_0: ┤ U2(φ,λ) ├
     └─────────┘

Matrix Representation:

\begin{split}U2(\phi, \lambda) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & -e^{i\lambda} \\ e^{i\phi} & e^{i(\phi+\lambda)} \end{pmatrix}\end{split}

Examples:

U2(\phi,\lambda) = e^{i \frac{\phi + \lambda}{2}}RZ(\phi) RY\left(\frac{\pi}{2}\right) RZ(\lambda) = e^{- i\frac{\pi}{4}} P\left(\frac{\pi}{2} + \phi\right) \sqrt{X} P\left(\lambda- \frac{\pi}{2}\right)

U2(0, \pi) = H

U2(0, 0) = RY(\pi/2)

U2(-\pi/2, \pi/2) = RX(\pi/2)

See also

U3Gate : U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses.

Create new U2 gate.

Attributes

condition_bits

Get Clbits in condition.

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

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.

Methods

inverse

inverse()

Return inverted U2 gate.

U2(\phi, \lambda)^{\dagger} =U2(-\lambda-\pi, -\phi+\pi)

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