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

# This code is part of Qiskit.
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# (C) Copyright IBM 2017.
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# 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
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"""Hadamard gate."""
from math import sqrt, pi
from typing import Optional, Union
import numpy
from qiskit.circuit.controlledgate import ControlledGate
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit._utils import with_gate_array, with_controlled_gate_array
from .t import TGate, TdgGate
from .s import SGate, SdgGate

_H_ARRAY = 1 / sqrt(2) * numpy.array([[1, 1], [1, -1]], dtype=numpy.complex128)


[documentos]@with_gate_array(_H_ARRAY) class HGate(Gate): r"""Single-qubit Hadamard gate. This gate is a \pi rotation about the X+Z axis, and has the effect of changing computation basis from :math:`|0\rangle,|1\rangle` to :math:`|+\rangle,|-\rangle` and vice-versa. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.h` method. **Circuit symbol:** .. parsed-literal:: 鈹屸攢鈹鈹鈹 q_0: 鈹 H 鈹 鈹斺攢鈹鈹鈹 **Matrix Representation:** .. math:: H = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix} """ def __init__(self, label: Optional[str] = None): """Create new H gate.""" super().__init__("h", 1, [], label=label) def _define(self): """ gate h a { u2(0,pi) a; } """ # pylint: disable=cyclic-import from qiskit.circuit.quantumcircuit import QuantumCircuit from .u2 import U2Gate q = QuantumRegister(1, "q") qc = QuantumCircuit(q, name=self.name) rules = [(U2Gate(0, pi), [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[int, str]] = None, ): """Return a (multi-)controlled-H gate. One control qubit returns a CH 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 = CHGate(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 H gate (itself).""" return HGate() # self-inverse
[documentos]@with_controlled_gate_array(_H_ARRAY, num_ctrl_qubits=1) class CHGate(ControlledGate): r"""Controlled-Hadamard gate. Applies a Hadamard on the target qubit if the control is in the :math:`|1\rangle` state. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.ch` method. **Circuit symbol:** .. parsed-literal:: q_0: 鈹鈹鈻犫攢鈹 鈹屸攢鈹粹攢鈹 q_1: 鈹 H 鈹 鈹斺攢鈹鈹鈹 **Matrix Representation:** .. math:: CH\ q_0, q_1 = I \otimes |0\rangle\langle 0| + H \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ 0 & 0 & 1 & 0 \\ 0 & \frac{1}{\sqrt{2}} & 0 & -\frac{1}{\sqrt{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 q_0: 鈹 H 鈹 鈹斺攢鈹攢鈹 q_1: 鈹鈹鈻犫攢鈹 .. math:: CH\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes H = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ 0 & 0 & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{pmatrix} """ def __init__(self, label: Optional[str] = None, ctrl_state: Optional[Union[int, str]] = None): """Create new CH gate.""" super().__init__( "ch", 2, [], num_ctrl_qubits=1, label=label, ctrl_state=ctrl_state, base_gate=HGate() ) def _define(self): """ gate ch a,b { s b; h b; t b; cx a, b; tdg b; h b; sdg b; } """ # pylint: disable=cyclic-import from qiskit.circuit.quantumcircuit import QuantumCircuit from .x import CXGate # pylint: disable=cyclic-import q = QuantumRegister(2, "q") qc = QuantumCircuit(q, name=self.name) rules = [ (SGate(), [q[1]], []), (HGate(), [q[1]], []), (TGate(), [q[1]], []), (CXGate(), [q[0], q[1]], []), (TdgGate(), [q[1]], []), (HGate(), [q[1]], []), (SdgGate(), [q[1]], []), ] for instr, qargs, cargs in rules: qc._append(instr, qargs, cargs) self.definition = qc
[documentos] def inverse(self): """Return inverted CH gate (itself).""" return CHGate(ctrl_state=self.ctrl_state) # self-inverse