# 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.
"""Z, CZ and CCZ gates."""
from typing import Optional, Union
import numpy
from qiskit.qasm import pi
from qiskit.circuit.controlledgate import ControlledGate
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit._utils import _compute_control_matrix
[documentos]class ZGate(Gate):
r"""The single-qubit Pauli-Z gate (:math:`\sigma_z`).
Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
with the :meth:`~qiskit.circuit.QuantumCircuit.z` method.
**Matrix Representation:**
.. math::
Z = \begin{pmatrix}
1 & 0 \\
0 & -1
\end{pmatrix}
**Circuit symbol:**
.. parsed-literal::
┌───┐
q_0: ┤ Z ├
└───┘
Equivalent to a :math:`\pi` radian rotation about the Z axis.
.. note::
A global phase difference exists between the definitions of
:math:`RZ(\pi)` and :math:`Z`.
.. math::
RZ(\pi) = \begin{pmatrix}
-1 & 0 \\
0 & 1
\end{pmatrix}
= -Z
The gate is equivalent to a phase flip.
.. math::
|0\rangle \rightarrow |0\rangle \\
|1\rangle \rightarrow -|1\rangle
"""
def __init__(self, label: Optional[str] = None):
"""Create new Z gate."""
super().__init__("z", 1, [], label=label)
def _define(self):
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .u1 import U1Gate
q = QuantumRegister(1, "q")
qc = QuantumCircuit(q, name=self.name)
rules = [(U1Gate(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[str, int]] = None,
):
"""Return a (multi-)controlled-Z gate.
One control returns a CZ 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 = CZGate(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):
"""Return inverted Z gate (itself)."""
return ZGate() # self-inverse
def __array__(self, dtype=None):
"""Return a numpy.array for the Z gate."""
return numpy.array([[1, 0], [0, -1]], dtype=dtype)
[documentos]class CZGate(ControlledGate):
r"""Controlled-Z gate.
This is a Clifford and symmetric gate.
Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
with the :meth:`~qiskit.circuit.QuantumCircuit.cz` method.
**Circuit symbol:**
.. parsed-literal::
q_0: ─■─
│
q_1: ─■─
**Matrix representation:**
.. math::
CZ\ q_0, q_1 =
I \otimes |0\rangle\langle 0| + Z \otimes |1\rangle\langle 1| =
\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & -1
\end{pmatrix}
In the computational basis, this gate flips the phase of
the target qubit if the control qubit is in the :math:`|1\rangle` state.
"""
def __init__(self, label: Optional[str] = None, ctrl_state: Optional[Union[str, int]] = None):
"""Create new CZ gate."""
super().__init__(
"cz", 2, [], label=label, num_ctrl_qubits=1, ctrl_state=ctrl_state, base_gate=ZGate()
)
def _define(self):
"""
gate cz a,b { h b; cx a,b; h b; }
"""
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .h import HGate
from .x import CXGate
q = QuantumRegister(2, "q")
qc = QuantumCircuit(q, name=self.name)
rules = [(HGate(), [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 inverted CZ gate (itself)."""
return CZGate(ctrl_state=self.ctrl_state) # self-inverse
def __array__(self, dtype=None):
"""Return a numpy.array for the CZ gate."""
if self.ctrl_state:
return numpy.array(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1]], dtype=dtype
)
else:
return numpy.array(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]], dtype=dtype
)
[documentos]class CCZGate(ControlledGate):
r"""CCZ gate.
This is a symmetric gate.
Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
with the :meth:`~qiskit.circuit.QuantumCircuit.ccz` method.
**Circuit symbol:**
.. parsed-literal::
q_0: ─■─
│
q_1: ─■─
│
q_2: ─■─
**Matrix representation:**
.. math::
CCZ\ q_0, q_1, q_2 =
I \otimes I \otimes |0\rangle\langle 0| + CZ \otimes |1\rangle\langle 1| =
\begin{pmatrix}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & -1
\end{pmatrix}
In the computational basis, this gate flips the phase of
the target qubit if the control qubits are in the :math:`|11\rangle` state.
"""
def __init__(self, label: Optional[str] = None, ctrl_state: Optional[Union[str, int]] = None):
"""Create new CCZ gate."""
super().__init__(
"ccz", 3, [], label=label, num_ctrl_qubits=2, ctrl_state=ctrl_state, base_gate=ZGate()
)
def _define(self):
"""
gate ccz a,b,c { h c; ccx a,b,c; h c; }
"""
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .h import HGate
from .x import CCXGate
q = QuantumRegister(3, "q")
qc = QuantumCircuit(q, name=self.name)
rules = [(HGate(), [q[2]], []), (CCXGate(), [q[0], q[1], q[2]], []), (HGate(), [q[2]], [])]
for instr, qargs, cargs in rules:
qc._append(instr, qargs, cargs)
self.definition = qc
[documentos] def inverse(self):
"""Return inverted CCZ gate (itself)."""
return CCZGate(ctrl_state=self.ctrl_state) # self-inverse
def __array__(self, dtype=None):
"""Return a numpy.array for the CCZ gate."""
mat = _compute_control_matrix(
self.base_gate.to_matrix(), self.num_ctrl_qubits, ctrl_state=self.ctrl_state
)
if dtype is not None:
return numpy.asarray(mat, dtype=dtype)
return mat