Source code for qiskit.circuit.library.standard_gates.z
# 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 and CZ gates."""
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
[docs]class ZGate(Gate):
r"""The single-qubit Pauli-Z gate (:math:`\sigma_z`).
**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=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
[docs] def control(self, num_ctrl_qubits=1, label=None, ctrl_state=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)
def __array__(self, dtype=None):
"""Return a numpy.array for the Z gate."""
return numpy.array([[1, 0], [0, -1]], dtype=dtype)
[docs]class CZGate(ControlledGate):
r"""Controlled-Z gate.
This is a Clifford and symmetric gate.
**Circuit symbol:**
.. parsed-literal::
q_0: ─■─
│
q_1: ─■─
**Matrix representation:**
.. math::
CZ\ q_1, q_0 =
|0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes Z =
\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=None, ctrl_state=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
[docs] 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
)