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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2019.","#","# This code is licensed under the Apache License, Version 2.0. You may","# obtain a copy of this license in the LICENSE.txt file in the root directory","# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.","#","# 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.","","\"\"\"Two-qubit XX-rotation gate.\"\"\"","import math","from typing import Optional","import numpy","from qiskit.circuit.gate import Gate","from qiskit.circuit.quantumregister import QuantumRegister","from qiskit.circuit.parameterexpression import ParameterValueType","","","class RXXGate(Gate):"," r\"\"\"A parametric 2-qubit :math:`X \\otimes X` interaction (rotation about XX).",""," This gate is symmetric, and is maximally entangling at :math:`\\theta = \\pi/2`.",""," Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`"," with the :meth:`~qiskit.circuit.QuantumCircuit.rxx` method.",""," **Circuit Symbol:**",""," .. parsed-literal::",""," ┌─────────┐"," q_0: ┤1 ├"," │ Rxx(ϴ) │"," q_1: ┤0 ├"," └─────────┘",""," **Matrix Representation:**",""," .. math::",""," \\newcommand{\\rotationangle}{\\frac{\\theta}{2}}",""," R_{XX}(\\theta) = \\exp\\left(-i \\rotationangle X{\\otimes}X\\right) ="," \\begin{pmatrix}"," \\cos\\left(\\rotationangle\\right) & 0 & 0 & -i\\sin\\left(\\rotationangle\\right) \\\\"," 0 & \\cos\\left(\\rotationangle\\right) & -i\\sin\\left(\\rotationangle\\right) & 0 \\\\"," 0 & -i\\sin\\left(\\rotationangle\\right) & \\cos\\left(\\rotationangle\\right) & 0 \\\\"," -i\\sin\\left(\\rotationangle\\right) & 0 & 0 & \\cos\\left(\\rotationangle\\right)"," \\end{pmatrix}",""," **Examples:**",""," .. math::",""," R_{XX}(\\theta = 0) = I",""," .. math::",""," R_{XX}(\\theta = \\pi) = i X \\otimes X",""," .. math::",""," R_{XX}\\left(\\theta = \\frac{\\pi}{2}\\right) = \\frac{1}{\\sqrt{2}}"," \\begin{pmatrix}"," 1 & 0 & 0 & -i \\\\"," 0 & 1 & -i & 0 \\\\"," 0 & -i & 1 & 0 \\\\"," -i & 0 & 0 & 1"," \\end{pmatrix}"," \"\"\"",""," def __init__("," self, theta: ParameterValueType, label: Optional[str] = None, *, duration=None, unit=\"dt\""," ):"," \"\"\"Create new RXX gate.\"\"\""," super().__init__(\"rxx\", 2, [theta], label=label, duration=duration, unit=unit)",""," def _define(self):"," \"\"\"Calculate a subcircuit that implements this unitary.\"\"\""," # pylint: disable=cyclic-import"," from qiskit.circuit.quantumcircuit import QuantumCircuit"," from .x import CXGate"," from .h import HGate"," from .rz import RZGate",""," # ┌───┐ ┌───┐"," # q_0: ┤ H ├──■─────────────■──┤ H ├"," # ├───┤┌─┴─┐┌───────┐┌─┴─┐├───┤"," # q_1: ┤ H ├┤ X ├┤ Rz(0) ├┤ X ├┤ H ├"," # └───┘└───┘└───────┘└───┘└───┘"," theta = self.params[0]"," q = QuantumRegister(2, \"q\")"," qc = QuantumCircuit(q, name=self.name)"," rules = ["," (HGate(), [q[0]], []),"," (HGate(), [q[1]], []),"," (CXGate(), [q[0], q[1]], []),"," (RZGate(theta), [q[1]], []),"," (CXGate(), [q[0], q[1]], []),"," (HGate(), [q[1]], []),"," (HGate(), [q[0]], []),"," ]"," for instr, qargs, cargs in rules:"," qc._append(instr, qargs, cargs)",""," self.definition = qc",""," def inverse(self, annotated: bool = False):"," \"\"\"Return inverse RXX gate (i.e. with the negative rotation angle).",""," Args:"," annotated: when set to ``True``, this is typically used to return an"," :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete"," :class:`.Gate`. 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