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# Source code for qiskit.circuit.library.standard_gates.u2

# This code is part of Qiskit.
#
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""One-pulse single-qubit gate."""
from math import sqrt, pi
from cmath import exp
from typing import Optional
import numpy
from qiskit.circuit.gate import Gate
from qiskit.circuit.parameterexpression import ParameterValueType
from qiskit.circuit.quantumregister import QuantumRegister

[docs]class U2Gate(Gate): r"""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 .. math:: U2(\phi, \lambda) = U\left(\frac{\pi}{2}, \phi, \lambda\right) .. code-block:: python circuit = QuantumCircuit(1) circuit.u(pi/2, phi, lambda) **Circuit symbol:** .. parsed-literal:: ┌─────────┐ q_0: ┤ U2(φ,λ) ├ └─────────┘ **Matrix Representation:** .. math:: U2(\phi, \lambda) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & -e^{i\lambda} \\ e^{i\phi} & e^{i(\phi+\lambda)} \end{pmatrix} **Examples:** .. math:: 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) .. math:: U2(0, \pi) = H .. math:: U2(0, 0) = RY(\pi/2) .. math:: U2(-\pi/2, \pi/2) = RX(\pi/2) .. seealso:: :class:~qiskit.circuit.library.standard_gates.U3Gate: U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses. """ def __init__( self, phi: ParameterValueType, lam: ParameterValueType, label: Optional[str] = None ): """Create new U2 gate.""" super().__init__("u2", 1, [phi, lam], label=label) def _define(self): # pylint: disable=cyclic-import from qiskit.circuit.quantumcircuit import QuantumCircuit from .u3 import U3Gate q = QuantumRegister(1, "q") qc = QuantumCircuit(q, name=self.name) rules = [(U3Gate(pi / 2, self.params[0], self.params[1]), [q[0]], [])] for instr, qargs, cargs in rules: qc._append(instr, qargs, cargs) self.definition = qc
[docs] def inverse(self): r"""Return inverted U2 gate. :math:U2(\phi, \lambda)^{\dagger} =U2(-\lambda-\pi, -\phi+\pi)) """ return U2Gate(-self.params[1] - pi, -self.params[0] + pi)
def __array__(self, dtype=complex): """Return a Numpy.array for the U2 gate.""" isqrt2 = 1 / sqrt(2) phi, lam = self.params phi, lam = float(phi), float(lam) return numpy.array( [ [isqrt2, -exp(1j * lam) * isqrt2], [exp(1j * phi) * isqrt2, exp(1j * (phi + lam)) * isqrt2], ], dtype=dtype, )