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This code is part of Qiskit.","#","# (C) Copyright IBM 2017.","#","# 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-pulse single-qubit gate.\"\"\"","import copy","import math","from cmath import exp","from typing import Optional, Union","import numpy","from qiskit.circuit.controlledgate import ControlledGate","from qiskit.circuit.gate import Gate","from qiskit.circuit.parameterexpression import ParameterValueType","from qiskit.circuit.quantumregister import QuantumRegister","","","class UGate(Gate):"," r\"\"\"Generic single-qubit rotation gate with 3 Euler angles.",""," Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`"," with the :meth:`~qiskit.circuit.QuantumCircuit.u` method.",""," **Circuit symbol:**",""," .. parsed-literal::",""," ┌──────────┐"," q_0: ┤ U(ϴ,φ,λ) ├"," └──────────┘",""," **Matrix Representation:**",""," .. math::",""," \\newcommand{\\rotationangle}{\\frac{\\theta}{2}}",""," U(\\theta, \\phi, \\lambda) ="," \\begin{pmatrix}"," \\cos\\left(\\rotationangle\\right) & -e^{i\\lambda}\\sin\\left(\\rotationangle\\right) \\\\"," e^{i\\phi}\\sin\\left(\\rotationangle\\right) & e^{i(\\phi+\\lambda)}\\cos\\left(\\rotationangle\\right)"," \\end{pmatrix}",""," .. note::",""," The matrix representation shown here is the same as in the `OpenQASM 3.0 specification"," `_,"," which differs from the `OpenQASM 2.0 specification"," `_ by a global phase of"," :math:`e^{i(\\phi+\\lambda)/2}`.",""," **Examples:**",""," .. math::",""," U\\left(\\theta, -\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right) = RX(\\theta)",""," .. math::",""," U(\\theta, 0, 0) = RY(\\theta)"," \"\"\"",""," def __init__("," self,"," theta: ParameterValueType,"," phi: ParameterValueType,"," lam: ParameterValueType,"," label: Optional[str] = None,"," *,"," duration=None,"," unit=\"dt\","," ):"," \"\"\"Create new U gate.\"\"\""," super().__init__(\"u\", 1, [theta, phi, lam], label=label, duration=duration, unit=unit)",""," def inverse(self, annotated: bool = False):"," r\"\"\"Return inverted U gate.",""," :math:`U(\\theta,\\phi,\\lambda)^{\\dagger} =U(-\\theta,-\\lambda,-\\phi))`",""," 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`. However, for this class this argument is ignored as the"," inverse of this gate is always a :class:`.UGate` with inverse parameter values.",""," Returns:"," UGate: inverse gate."," \"\"\""," return UGate(-self.params[0], -self.params[2], -self.params[1])",""," def control("," self,"," num_ctrl_qubits: int = 1,"," label: Optional[str] = None,"," ctrl_state: Optional[Union[str, int]] = None,"," annotated: bool = False,"," ):"," \"\"\"Return a (multi-)controlled-U gate.",""," Args:"," num_ctrl_qubits: number of control qubits."," label: An optional label for the gate [Default: ``None``]"," ctrl_state: control state expressed as integer,"," string (e.g.``'110'``), or ``None``. If ``None``, use all 1s."," annotated: indicates whether the controlled gate can be implemented"," as an annotated gate.",""," Returns:"," ControlledGate: controlled version of this gate."," \"\"\""," if not annotated and num_ctrl_qubits == 1:"," gate = CUGate("," self.params[0],"," self.params[1],"," self.params[2],"," 0,"," label=label,"," ctrl_state=ctrl_state,"," )"," gate.base_gate.label = self.label"," else:"," gate = super().control("," num_ctrl_qubits=num_ctrl_qubits,"," label=label,"," ctrl_state=ctrl_state,"," annotated=annotated,"," )"," return gate",""," def __array__(self, dtype=complex):"," \"\"\"Return a numpy.array for the U gate.\"\"\""," theta, phi, lam = (float(param) for param in self.params)"," cos = math.cos(theta / 2)"," sin = math.sin(theta / 2)"," return numpy.array("," ["," [cos, -exp(1j * lam) * sin],"," [exp(1j * phi) * sin, exp(1j * (phi + lam)) * cos],"," ],"," dtype=dtype,"," )",""," def __eq__(self, other):"," if isinstance(other, UGate):"," return self._compare_parameters(other)"," return False","","","class _CUGateParams(list):"," # This awful class is to let `CUGate.params` have its keys settable (as"," # `QuantumCircuit.assign_parameters` requires), while accounting for the problem that `CUGate`"," # was defined to have a different number of parameters to its `base_gate`, which breaks"," # `ControlledGate`'s assumptions, and would make most parametric `CUGate`s invalid."," #"," # It's constructed only as part of the `CUGate.params` getter, and given that the general"," # circuit model assumes that that's a directly mutable list that _must_ be kept in sync with the"," # gate's requirements, we don't need this to support arbitrary mutation, just enough for"," # `QuantumCircuit.assign_parameters` to work.",""," __slots__ = (\"_gate\",)",""," def __init__(self, gate):"," super().__init__(gate._params)"," self._gate = gate",""," def __setitem__(self, key, value):"," super().__setitem__(key, value)"," self._gate._params[key] = value"," # Magic numbers: CUGate has 4 parameters, UGate has 3, with the last of CUGate's missing."," if isinstance(key, slice):"," # We don't need to worry about the case of the slice being used to insert extra / remove"," # elements because that would be \"undefined behaviour\" in a gate already, so we're"," # within our rights to do anything at all."," for i, base_key in enumerate(range(*key.indices(4))):"," if base_key < 0:"," base_key = 4 + base_key"," if base_key < 3:"," self._gate.base_gate.params[base_key] = value[i]"," else:"," if key < 0:"," key = 4 + key"," if key < 3:"," self._gate.base_gate.params[key] = value","","","class CUGate(ControlledGate):"," r\"\"\"Controlled-U gate (4-parameter two-qubit gate).",""," This is a controlled version of the U gate (generic single qubit rotation),"," including a possible global phase :math:`e^{i\\gamma}` of the U gate.",""," Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`"," with the :meth:`~qiskit.circuit.QuantumCircuit.cu` method.",""," **Circuit symbol:**",""," .. parsed-literal::",""," q_0: ──────■──────"," ┌─────┴──────┐"," q_1: ┤ U(ϴ,φ,λ,γ) ├"," └────────────┘",""," **Matrix representation:**",""," .. math::",""," \\newcommand{\\rotationangle}{\\frac{\\theta}{2}}",""," CU(\\theta, \\phi, \\lambda, \\gamma)\\ q_0, q_1 ="," I \\otimes |0\\rangle\\langle 0| +"," e^{i\\gamma} U(\\theta,\\phi,\\lambda) \\otimes |1\\rangle\\langle 1| ="," \\begin{pmatrix}"," 1 & 0 & 0 & 0 \\\\"," 0 & e^{i\\gamma}\\cos(\\rotationangle) &"," 0 & -e^{i(\\gamma + \\lambda)}\\sin(\\rotationangle) \\\\"," 0 & 0 & 1 & 0 \\\\"," 0 & e^{i(\\gamma+\\phi)}\\sin(\\rotationangle) &"," 0 & e^{i(\\gamma+\\phi+\\lambda)}\\cos(\\rotationangle)"," \\end{pmatrix}",""," .. note::",""," In Qiskit's convention, higher qubit indices are more significant"," (little endian convention). In many textbooks, controlled gates are"," presented with the assumption of more significant qubits as control,"," which in our case would be q_1. Thus a textbook matrix for this"," gate will be:",""," .. parsed-literal::"," ┌────────────┐"," q_0: ┤ U(ϴ,φ,λ,γ) ├"," └─────┬──────┘"," q_1: ──────■───────",""," .. math::",""," \\newcommand{\\rotationangle}{\\frac{\\theta}{2}}"," CU(\\theta, \\phi, \\lambda, \\gamma)\\ q_1, q_0 ="," |0\\rangle\\langle 0| \\otimes I +"," e^{i\\gamma}|1\\rangle\\langle 1| \\otimes U(\\theta,\\phi,\\lambda) ="," \\begin{pmatrix}"," 1 & 0 & 0 & 0 \\\\"," 0 & 1 & 0 & 0 \\\\"," 0 & 0 & e^{i\\gamma} \\cos(\\rotationangle) & -e^{i(\\gamma + \\lambda)}\\sin(\\rotationangle) \\\\"," 0 & 0 &"," e^{i(\\gamma + \\phi)}\\sin(\\rotationangle) & e^{i(\\gamma + \\phi+\\lambda)}\\cos(\\rotationangle)"," \\end{pmatrix}"," \"\"\"",""," def __init__("," self,"," theta: ParameterValueType,"," phi: ParameterValueType,"," lam: ParameterValueType,"," gamma: ParameterValueType,"," label: Optional[str] = None,"," ctrl_state: Optional[Union[str, int]] = None,"," *,"," duration=None,"," unit=\"dt\","," _base_label=None,"," ):"," \"\"\"Create new CU gate.\"\"\""," super().__init__("," \"cu\","," 2,"," [theta, phi, lam, gamma],"," num_ctrl_qubits=1,"," label=label,"," ctrl_state=ctrl_state,"," base_gate=UGate(theta, phi, lam, label=_base_label),"," duration=duration,"," unit=unit,"," )",""," def _define(self):"," \"\"\""," gate cu(theta,phi,lambda,gamma) c, t"," { phase(gamma) c;"," phase((lambda+phi)/2) c;"," phase((lambda-phi)/2) t;"," cx c,t;"," u(-theta/2,0,-(phi+lambda)/2) t;"," cx c,t;"," u(theta/2,phi,0) t;"," }"," \"\"\""," # pylint: disable=cyclic-import"," from qiskit.circuit.quantumcircuit import QuantumCircuit",""," # ┌──────┐ ┌──────────────┐"," # q_0: ────┤ P(γ) ├────┤ P(λ/2 + φ/2) ├──■────────────────────────────■────────────────"," # ┌───┴──────┴───┐└──────────────┘┌─┴─┐┌──────────────────────┐┌─┴─┐┌────────────┐"," # q_1: ┤ P(λ/2 - φ/2) ├────────────────┤ X ├┤ U(-0/2,0,-λ/2 - φ/2) ├┤ X ├┤ U(0/2,φ,0) ├"," # └──────────────┘ └───┘└──────────────────────┘└───┘└────────────┘"," q = QuantumRegister(2, \"q\")"," qc = QuantumCircuit(q, name=self.name)"," qc.p(self.params[3], 0)"," qc.p((self.params[2] + self.params[1]) / 2, 0)"," qc.p((self.params[2] - self.params[1]) / 2, 1)"," qc.cx(0, 1)"," qc.u(-self.params[0] / 2, 0, -(self.params[1] + self.params[2]) / 2, 1)"," qc.cx(0, 1)"," qc.u(self.params[0] / 2, self.params[1], 0, 1)"," self.definition = qc",""," def inverse(self, annotated: bool = False):"," r\"\"\"Return inverted CU gate.",""," :math:`CU(\\theta,\\phi,\\lambda,\\gamma)^{\\dagger} = CU(-\\theta,-\\phi,-\\lambda,-\\gamma))`",""," 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`. However, for this class this argument is ignored as the inverse"," of this gate is always a :class:`.CUGate` with inverse parameter"," values.",""," Returns:"," CUGate: inverse gate."," \"\"\""," return CUGate("," -self.params[0],"," -self.params[2],"," -self.params[1],"," -self.params[3],"," ctrl_state=self.ctrl_state,"," )",""," def __array__(self, dtype=None):"," \"\"\"Return a numpy.array for the CU gate.\"\"\""," theta, phi, lam, gamma = (float(param) for param in self.params)"," cos = numpy.cos(theta / 2)"," sin = numpy.sin(theta / 2)"," a = numpy.exp(1j * gamma) * cos"," b = -numpy.exp(1j * (gamma + lam)) * sin"," c = numpy.exp(1j * (gamma + phi)) * sin"," d = numpy.exp(1j * (gamma + phi + lam)) * cos"," if self.ctrl_state:"," return numpy.array("," [[1, 0, 0, 0], [0, a, 0, b], [0, 0, 1, 0], [0, c, 0, d]], dtype=dtype"," )"," else:"," return numpy.array("," [[a, 0, b, 0], [0, 1, 0, 0], [c, 0, d, 0], [0, 0, 0, 1]], dtype=dtype"," )",""," @property"," def params(self):"," return _CUGateParams(self)",""," @params.setter"," def params(self, parameters):"," # We need to skip `ControlledGate` in the inheritance tree, since it defines"," # that all controlled gates are `(1-|c>