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

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"""Two-qubit ZX-rotation gate."""
import math
from typing import Optional
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit.parameterexpression import ParameterValueType


[documentos]class RZXGate(Gate): r"""A parametric 2-qubit :math:`Z \otimes X` interaction (rotation about ZX). This gate is maximally entangling at :math:`\theta = \pi/2`. The cross-resonance gate (CR) for superconducting qubits implements a ZX interaction (however other terms are also present in an experiment). Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.rzx` method. **Circuit Symbol:** .. parsed-literal:: 鈹屸攢鈹鈹鈹鈹鈹鈹鈹鈹鈹 q_0: 鈹0 鈹 鈹 Rzx(胃) 鈹 q_1: 鈹1 鈹 鈹斺攢鈹鈹鈹鈹鈹鈹鈹鈹鈹 **Matrix Representation:** .. math:: \newcommand{\th}{\frac{\theta}{2}} R_{ZX}(\theta)\ q_0, q_1 = \exp\left(-i \frac{\theta}{2} X{\otimes}Z\right) = \begin{pmatrix} \cos\left(\th\right) & 0 & -i\sin\left(\th\right) & 0 \\ 0 & \cos\left(\th\right) & 0 & i\sin\left(\th\right) \\ -i\sin\left(\th\right) & 0 & \cos\left(\th\right) & 0 \\ 0 & i\sin\left(\th\right) & 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 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:: 鈹屸攢鈹鈹鈹鈹鈹鈹鈹鈹鈹 q_0: 鈹1 鈹 鈹 Rzx(胃) 鈹 q_1: 鈹0 鈹 鈹斺攢鈹鈹鈹鈹鈹鈹鈹鈹鈹 .. math:: \newcommand{\th}{\frac{\theta}{2}} R_{ZX}(\theta)\ q_1, q_0 = exp(-i \frac{\theta}{2} Z{\otimes}X) = \begin{pmatrix} \cos(\th) & -i\sin(\th) & 0 & 0 \\ -i\sin(\th) & \cos(\th) & 0 & 0 \\ 0 & 0 & \cos(\th) & i\sin(\th) \\ 0 & 0 & i\sin(\th) & \cos(\th) \end{pmatrix} This is a direct sum of RX rotations, so this gate is equivalent to a uniformly controlled (multiplexed) RX gate: .. math:: R_{ZX}(\theta)\ q_1, q_0 = \begin{pmatrix} RX(\theta) & 0 \\ 0 & RX(-\theta) \end{pmatrix} **Examples:** .. math:: R_{ZX}(\theta = 0) = I .. math:: R_{ZX}(\theta = 2\pi) = -I .. math:: R_{ZX}(\theta = \pi) = -i Z \otimes X .. math:: RZX(\theta = \frac{\pi}{2}) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 0 & -i & 0 \\ 0 & 1 & 0 & i \\ -i & 0 & 1 & 0 \\ 0 & i & 0 & 1 \end{pmatrix} """ def __init__(self, theta: ParameterValueType, label: Optional[str] = None): """Create new RZX gate.""" super().__init__("rzx", 2, [theta], label=label) def _define(self): """ gate rzx(theta) a, b { h b; cx a, b; u1(theta) b; cx a, b; h b;} """ # pylint: disable=cyclic-import from qiskit.circuit.quantumcircuit import QuantumCircuit from .h import HGate from .x import CXGate from .rz import RZGate # q_0: 鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹 # 鈹屸攢鈹鈹鈹愨攲鈹鈹粹攢鈹愨攲鈹鈹鈹鈹鈹鈹鈹鈹愨攲鈹鈹粹攢鈹愨攲鈹鈹鈹鈹 # q_1: 鈹 H 鈹溾敜 X 鈹溾敜 Rz(0) 鈹溾敜 X 鈹溾敜 H 鈹 # 鈹斺攢鈹鈹鈹樷敂鈹鈹鈹鈹樷敂鈹鈹鈹鈹鈹鈹鈹鈹樷敂鈹鈹鈹鈹樷敂鈹鈹鈹鈹 theta = self.params[0] q = QuantumRegister(2, "q") qc = QuantumCircuit(q, name=self.name) rules = [ (HGate(), [q[1]], []), (CXGate(), [q[0], q[1]], []), (RZGate(theta), [q[1]], []), (CXGate(), [q[0], q[1]], []), (HGate(), [q[1]], []), ] for instr, qargs, cargs in rules: qc._append(instr, qargs, cargs) self.definition = qc
[documentos] def inverse(self): """Return inverse RZX gate (i.e. with the negative rotation angle).""" return RZXGate(-self.params[0])
def __array__(self, dtype=None): """Return a numpy.array for the RZX gate.""" import numpy half_theta = float(self.params[0]) / 2 cos = math.cos(half_theta) isin = 1j * math.sin(half_theta) return numpy.array( [[cos, 0, -isin, 0], [0, cos, 0, isin], [-isin, 0, cos, 0], [0, isin, 0, cos]], dtype=dtype, )
[documentos] def power(self, exponent: float): """Raise gate to a power.""" (theta,) = self.params return RZXGate(exponent * theta)