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

# 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.

"""Rotation around the Z axis."""
from cmath import exp
from typing import Optional, Union
from qiskit.circuit.gate import Gate
from qiskit.circuit.controlledgate import ControlledGate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit.parameterexpression import ParameterValueType


[documentos]class RZGate(Gate): r"""Single-qubit rotation about the Z axis. This is a diagonal gate. It can be implemented virtually in hardware via framechanges (i.e. at zero error and duration). Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.rz` method. **Circuit symbol:** .. parsed-literal:: 鈹屸攢鈹鈹鈹鈹鈹鈹鈹 q_0: 鈹 Rz(位) 鈹 鈹斺攢鈹鈹鈹鈹鈹鈹鈹 **Matrix Representation:** .. math:: RZ(\lambda) = \exp\left(-i\frac{\lambda}{2}Z\right) = \begin{pmatrix} e^{-i\frac{\lambda}{2}} & 0 \\ 0 & e^{i\frac{\lambda}{2}} \end{pmatrix} .. seealso:: :class:`~qiskit.circuit.library.standard_gates.U1Gate` This gate is equivalent to U1 up to a phase factor. .. math:: U1(\lambda) = e^{i{\lambda}/2}RZ(\lambda) Reference for virtual Z gate implementation: `1612.00858 <https://arxiv.org/abs/1612.00858>`_ """ def __init__(self, phi: ParameterValueType, label: Optional[str] = None): """Create new RZ gate.""" super().__init__("rz", 1, [phi], label=label) def _define(self): """ gate rz(phi) a { u1(phi) a; } """ # pylint: disable=cyclic-import from qiskit.circuit.quantumcircuit import QuantumCircuit from .u1 import U1Gate q = QuantumRegister(1, "q") theta = self.params[0] qc = QuantumCircuit(q, name=self.name, global_phase=-theta / 2) rules = [(U1Gate(theta), [q[0]], [])] for instr, qargs, cargs in rules: qc._append(instr, qargs, cargs) self.definition = qc
[documentos] def control( self, num_ctrl_qubits: int = 1, label: Optional[str] = None, ctrl_state: Optional[Union[str, int]] = None, ): """Return a (multi-)controlled-RZ gate. Args: num_ctrl_qubits (int): number of control qubits. label (str or None): An optional label for the gate [Default: None] ctrl_state (int or str or None): control state expressed as integer, string (e.g. '110'), or None. If None, use all 1s. Returns: ControlledGate: controlled version of this gate. """ if num_ctrl_qubits == 1: gate = CRZGate(self.params[0], label=label, ctrl_state=ctrl_state) gate.base_gate.label = self.label return gate return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label, ctrl_state=ctrl_state)
[documentos] def inverse(self): r"""Return inverted RZ gate :math:`RZ(\lambda)^{\dagger} = RZ(-\lambda)` """ return RZGate(-self.params[0])
def __array__(self, dtype=None): """Return a numpy.array for the RZ gate.""" import numpy as np ilam2 = 0.5j * float(self.params[0]) return np.array([[exp(-ilam2), 0], [0, exp(ilam2)]], dtype=dtype)
[documentos] def power(self, exponent: float): """Raise gate to a power.""" (theta,) = self.params return RZGate(exponent * theta)
[documentos]class CRZGate(ControlledGate): r"""Controlled-RZ gate. This is a diagonal but non-symmetric gate that induces a phase on the state of the target qubit, depending on the control state. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.crz` method. **Circuit symbol:** .. parsed-literal:: q_0: 鈹鈹鈹鈹鈻犫攢鈹鈹鈹 鈹屸攢鈹鈹鈹粹攢鈹鈹鈹 q_1: 鈹 Rz(位) 鈹 鈹斺攢鈹鈹鈹鈹鈹鈹鈹 **Matrix representation:** .. math:: CRZ(\lambda)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + RZ(\lambda) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & e^{-i\frac{\lambda}{2}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\frac{\lambda}{2}} \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:: 鈹屸攢鈹鈹鈹鈹鈹鈹鈹 q_0: 鈹 Rz(位) 鈹 鈹斺攢鈹鈹鈹攢鈹鈹鈹 q_1: 鈹鈹鈹鈹鈻犫攢鈹鈹鈹 .. math:: CRZ(\lambda)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes RZ(\lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{-i\frac{\lambda}{2}} & 0 \\ 0 & 0 & 0 & e^{i\frac{\lambda}{2}} \end{pmatrix} .. seealso:: :class:`~qiskit.circuit.library.standard_gates.CU1Gate`: Due to the global phase difference in the matrix definitions of U1 and RZ, CU1 and CRZ are different gates with a relative phase difference. """ def __init__( self, theta: ParameterValueType, label: Optional[str] = None, ctrl_state: Optional[Union[str, int]] = None, ): """Create new CRZ gate.""" super().__init__( "crz", 2, [theta], num_ctrl_qubits=1, label=label, ctrl_state=ctrl_state, base_gate=RZGate(theta), ) def _define(self): """ gate crz(lambda) a,b { rz(lambda/2) b; cx a,b; rz(-lambda/2) b; cx a,b; } """ # pylint: disable=cyclic-import from qiskit.circuit.quantumcircuit import QuantumCircuit from .x import CXGate # q_0: 鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹 # 鈹屸攢鈹鈹鈹鈹鈹鈹鈹鈹鈹愨攲鈹鈹粹攢鈹愨攲鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹愨攲鈹鈹粹攢鈹 # q_1: 鈹 Rz(位/2) 鈹溾敜 X 鈹溾敜 Rz(-位/2) 鈹溾敜 X 鈹 # 鈹斺攢鈹鈹鈹鈹鈹鈹鈹鈹鈹樷敂鈹鈹鈹鈹樷敂鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹樷敂鈹鈹鈹鈹 q = QuantumRegister(2, "q") qc = QuantumCircuit(q, name=self.name) rules = [ (RZGate(self.params[0] / 2), [q[1]], []), (CXGate(), [q[0], q[1]], []), (RZGate(-self.params[0] / 2), [q[1]], []), (CXGate(), [q[0], q[1]], []), ] for instr, qargs, cargs in rules: qc._append(instr, qargs, cargs) self.definition = qc
[documentos] def inverse(self): """Return inverse CRZ gate (i.e. with the negative rotation angle).""" return CRZGate(-self.params[0], ctrl_state=self.ctrl_state)
def __array__(self, dtype=None): """Return a numpy.array for the CRZ gate.""" import numpy arg = 1j * float(self.params[0]) / 2 if self.ctrl_state: return numpy.array( [[1, 0, 0, 0], [0, exp(-arg), 0, 0], [0, 0, 1, 0], [0, 0, 0, exp(arg)]], dtype=dtype, ) else: return numpy.array( [[exp(-arg), 0, 0, 0], [0, 1, 0, 0], [0, 0, exp(arg), 0], [0, 0, 0, 1]], dtype=dtype, )