C贸digo fuente para qiskit.circuit.library.standard_gates.xx_minus_yy

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# (C) Copyright IBM 2021.
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# This code is licensed under the Apache License, Version 2.0. You may
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"""Two-qubit XX-YY gate."""
import math
from cmath import exp
from math import pi
from typing import Optional

import numpy as np

from qiskit.circuit.gate import Gate
from qiskit.circuit.library.standard_gates.ry import RYGate
from qiskit.circuit.library.standard_gates.rz import RZGate
from qiskit.circuit.library.standard_gates.s import SdgGate, SGate
from qiskit.circuit.library.standard_gates.sx import SXdgGate, SXGate
from qiskit.circuit.library.standard_gates.x import CXGate
from qiskit.circuit.parameterexpression import ParameterValueType
from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.circuit.quantumregister import QuantumRegister


[documentos]class XXMinusYYGate(Gate): r"""XX-YY interaction gate. A 2-qubit parameterized XX-YY interaction. Its action is to induce a coherent rotation by some angle between :math:`|00\rangle` and :math:`|11\rangle`. **Circuit Symbol:** .. parsed-literal:: 鈹屸攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹 q_0: 鈹0 鈹 鈹 (XX-YY)(胃,尾) 鈹 q_1: 鈹1 鈹 鈹斺攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹 **Matrix Representation:** .. math:: \newcommand{\th}{\frac{\theta}{2}} R_{XX-YY}(\theta, \beta) q_0, q_1 = RZ_1(\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX-YY}{2}\right) \cdot RZ_1(-\beta) = \begin{pmatrix} \cos\left(\th\right) & 0 & 0 & -i\sin\left(\th\right)e^{-i\beta} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ -i\sin\left(\th\right)e^{i\beta} & 0 & 0 & \cos\left(\th\right) \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 adding the (optional) phase defined by :math:`beta` on q_1. Instead, if we apply it on (q_1, q_0), the phase is added on q_0. If :math:`beta` is set to its default value of :math:`0`, the gate is equivalent in big and little endian. .. parsed-literal:: 鈹屸攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹 q_0: 鈹1 鈹 鈹 (XX-YY)(胃,尾) 鈹 q_1: 鈹0 鈹 鈹斺攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹 .. math:: \newcommand{\th}{\frac{\theta}{2}} R_{XX-YY}(\theta, \beta) q_1, q_0 = RZ_0(\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX-YY}{2}\right) \cdot RZ_0(-\beta) = \begin{pmatrix} \cos\left(\th\right) & 0 & 0 & -i\sin\left(\th\right)e^{i\beta} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ -i\sin\left(\th\right)e^{-i\beta} & 0 & 0 & \cos\left(\th\right) \end{pmatrix} """ def __init__( self, theta: ParameterValueType, beta: ParameterValueType = 0, label: Optional[str] = "(XX-YY)", ): """Create new XX-YY gate. Args: theta: The rotation angle. beta: The phase angle. label: The label of the gate. """ super().__init__("xx_minus_yy", 2, [theta, beta], label=label) def _define(self): """ gate xx_minus_yy(theta, beta) a, b { rz(-beta) b; rz(-pi/2) a; sx a; rz(pi/2) a; s b; cx a, b; ry(theta/2) a; ry(-theta/2) b; cx a, b; sdg b; rz(-pi/2) a; sxdg a; rz(pi/2) a; rz(beta) b; } """ theta, beta = self.params register = QuantumRegister(2, "q") circuit = QuantumCircuit(register, name=self.name) a, b = register rules = [ (RZGate(-beta), [b], []), (RZGate(-pi / 2), [a], []), (SXGate(), [a], []), (RZGate(pi / 2), [a], []), (SGate(), [b], []), (CXGate(), [a, b], []), (RYGate(theta / 2), [a], []), (RYGate(-theta / 2), [b], []), (CXGate(), [a, b], []), (SdgGate(), [b], []), (RZGate(-pi / 2), [a], []), (SXdgGate(), [a], []), (RZGate(pi / 2), [a], []), (RZGate(beta), [b], []), ] for instr, qargs, cargs in rules: circuit._append(instr, qargs, cargs) self.definition = circuit
[documentos] def inverse(self): """Inverse gate.""" theta, beta = self.params return XXMinusYYGate(-theta, beta)
def __array__(self, dtype=complex): """Gate matrix.""" theta, beta = self.params cos = math.cos(theta / 2) sin = math.sin(theta / 2) return np.array( [ [cos, 0, 0, -1j * sin * exp(-1j * beta)], [0, 1, 0, 0], [0, 0, 1, 0], [-1j * sin * exp(1j * beta), 0, 0, cos], ], dtype=dtype, )
[documentos] def power(self, exponent: float): """Raise gate to a power.""" theta, beta = self.params return XXMinusYYGate(exponent * theta, beta)