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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, CZ and CCZ gates."""

from typing import Optional, Union

import numpy

from qiskit.circuit._utils import _compute_control_matrix
from qiskit.circuit.controlledgate import ControlledGate
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.qasm import pi

from .p import PhaseGate


[docs]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
[docs] 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)
[docs] 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)
[docs] def power(self, exponent: float): """Raise gate to a power.""" return PhaseGate(numpy.pi * exponent)
[docs]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
[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 )
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 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