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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2021.","#","# 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 ZX-rotation gate.\"\"\"","from math import sqrt","import numpy as np","","from qiskit.circuit._utils import with_gate_array","from qiskit.circuit.quantumregister import QuantumRegister","from qiskit.circuit.singleton import SingletonGate, stdlib_singleton_key","from .rzx import RZXGate","from .x import XGate","","","@with_gate_array("," sqrt(0.5) * np.array([[0, 1, 0, 1.0j], [1, 0, -1.0j, 0], [0, 1.0j, 0, 1], [-1.0j, 0, 1, 0]])",")","class ECRGate(SingletonGate):"," r\"\"\"An echoed cross-resonance gate.",""," This gate is maximally entangling and is equivalent to a CNOT up to"," single-qubit pre-rotations. The echoing procedure mitigates some"," unwanted terms (terms other than ZX) to cancel in an experiment."," More specifically, this gate implements :math:`\\frac{1}{\\sqrt{2}}(IX-XY)`.",""," Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`"," with the :meth:`~qiskit.circuit.QuantumCircuit.ecr` method.",""," **Circuit Symbol:**",""," .. parsed-literal::",""," ┌─────────┐ ┌────────────┐┌────────┐┌─────────────┐"," q_0: ┤0 ├ q_0: ┤0 ├┤ RX(pi) ├┤0 ├"," │ ECR │ = │ RZX(pi/4) │└────────┘│ RZX(-pi/4) │"," q_1: ┤1 ├ q_1: ┤1 ├──────────┤1 ├"," └─────────┘ └────────────┘ └─────────────┘",""," **Matrix Representation:**",""," .. math::",""," ECR\\ q_0, q_1 = \\frac{1}{\\sqrt{2}}"," \\begin{pmatrix}"," 0 & 1 & 0 & i \\\\"," 1 & 0 & -i & 0 \\\\"," 0 & i & 0 & 1 \\\\"," -i & 0 & 1 & 0"," \\end{pmatrix}",""," .. note::",""," In Qiskit's convention, higher qubit indices are more significant"," (little endian convention). In the above example we apply the gate"," on (q_0, q_1) which results in the :math:`X \\otimes Z` tensor order."," Instead, if we apply it on (q_1, q_0), the matrix will"," be :math:`Z \\otimes X`:",""," .. parsed-literal::",""," ┌─────────┐"," q_0: ┤1 ├"," │ ECR │"," q_1: ┤0 ├"," └─────────┘",""," .. math::",""," ECR\\ q_0, q_1 = \\frac{1}{\\sqrt{2}}"," \\begin{pmatrix}"," 0 & 0 & 1 & i \\\\"," 0 & 0 & i & 1 \\\\"," 1 & -i & 0 & 0 \\\\"," -i & 1 & 0 & 0"," \\end{pmatrix}"," \"\"\"",""," def __init__(self, label=None, *, duration=None, unit=\"dt\"):"," \"\"\"Create new ECR gate.\"\"\""," super().__init__(\"ecr\", 2, [], label=label, duration=duration, unit=unit)",""," _singleton_lookup_key = stdlib_singleton_key()",""," def _define(self):"," \"\"\""," gate ecr a, b { rzx(pi/4) a, b; x a; rzx(-pi/4) a, b;}"," \"\"\""," # pylint: disable=cyclic-import"," from qiskit.circuit.quantumcircuit import QuantumCircuit",""," q = QuantumRegister(2, \"q\")"," qc = QuantumCircuit(q, name=self.name)"," rules = ["," (RZXGate(np.pi / 4), [q[0], q[1]], []),"," (XGate(), [q[0]], []),"," (RZXGate(-np.pi / 4), [q[0], q[1]], []),"," ]"," for instr, qargs, cargs in rules:"," qc._append(instr, qargs, cargs)",""," self.definition = qc",""," def inverse(self, annotated: bool = False):"," \"\"\"Return inverse ECR gate (itself).",""," 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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