# 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.
"""Phase Gate."""
import numpy
from qiskit.circuit.controlledgate import ControlledGate
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
[docs]class PhaseGate(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).
**Circuit symbol:**
.. parsed-literal::
┌──────┐
q_0: ┤ P(λ) ├
└──────┘
**Matrix Representation:**
.. math::
P(\lambda) =
\begin{pmatrix}
1 & 0 \\
0 & e^{i\lambda}
\end{pmatrix}
**Examples:**
.. math::
P(\lambda = \pi) = Z
.. math::
P(\lambda = \pi/2) = S
.. math::
P(\lambda = \pi/4) = T
.. seealso::
:class:`~qiskit.circuit.library.standard_gates.RZGate`:
This gate is equivalent to RZ up to a phase factor.
.. math::
P(\lambda) = e^{i{\lambda}/2} RZ(\lambda)
Reference for virtual Z gate implementation:
`1612.00858 <https://arxiv.org/abs/1612.00858>`_
"""
[docs] def __init__(self, theta, label=None):
"""Create new Phase gate."""
super().__init__('p', 1, [theta], label=label)
def _define(self):
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .u import UGate
q = QuantumRegister(1, 'q')
qc = QuantumCircuit(q, name=self.name)
qc.append(UGate(0, 0, self.params[0]), [0])
self.definition = qc
[docs] def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
"""Return a (mutli-)controlled-Phase 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 = CPhaseGate(self.params[0], label=label, ctrl_state=ctrl_state)
elif ctrl_state is None and num_ctrl_qubits > 1:
gate = MCPhaseGate(self.params[0], num_ctrl_qubits, label=label)
else:
return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
ctrl_state=ctrl_state)
gate.base_gate.label = self.label
return gate
[docs] def inverse(self):
r"""Return inverted Phase gate (:math:`Phase(\lambda){\dagger} = Phase(-\lambda)`)"""
return PhaseGate(-self.params[0])
[docs] def to_matrix(self):
"""Return a numpy.array for the Phase gate."""
lam = float(self.params[0])
return numpy.array([[1, 0], [0, numpy.exp(1j * lam)]], dtype=complex)
[docs]class CPhaseGate(ControlledGate):
r"""Controlled-Phase gate.
This is a diagonal and symmetric gate that induces a
phase on the state of the target qubit, depending on the control state.
**Circuit symbol:**
.. parsed-literal::
q_0: ─■──
│λ
q_1: ─■──
**Matrix representation:**
.. math::
CPhase =
|0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes P =
\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & e^{i\lambda}
\end{pmatrix}
.. seealso::
:class:`~qiskit.circuit.library.standard_gates.CRZGate`:
Due to the global phase difference in the matrix definitions
of Phase and RZ, CPhase and CRZ are different gates with a relative
phase difference.
"""
[docs] def __init__(self, theta, label=None, ctrl_state=None):
"""Create new CPhase gate."""
super().__init__('cp', 2, [theta], num_ctrl_qubits=1, label=label,
ctrl_state=ctrl_state, base_gate=PhaseGate(theta))
def _define(self):
"""
gate cphase(lambda) a,b
{ phase(lambda/2) a; cx a,b;
phase(-lambda/2) b; cx a,b;
phase(lambda/2) b;
}
"""
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
q = QuantumRegister(2, 'q')
qc = QuantumCircuit(q, name=self.name)
qc.p(self.params[0] / 2, 0)
qc.cx(0, 1)
qc.p(-self.params[0] / 2, 1)
qc.cx(0, 1)
qc.p(self.params[0] / 2, 1)
self.definition = qc
[docs] def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
"""Controlled version of this 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 ctrl_state is None:
gate = MCPhaseGate(self.params[0], num_ctrl_qubits=num_ctrl_qubits + 1, label=label)
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):
r"""Return inverted CPhase gate (:math:`CPhase(\lambda){\dagger} = CPhase(-\lambda)`)"""
return CPhaseGate(-self.params[0], ctrl_state=self.ctrl_state)
[docs] def to_matrix(self):
"""Return a numpy.array for the CPhase gate."""
eith = numpy.exp(1j * float(self.params[0]))
if self.ctrl_state:
return numpy.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, eith]],
dtype=complex)
return numpy.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, eith, 0],
[0, 0, 0, 1]],
dtype=complex)
[docs]class MCPhaseGate(ControlledGate):
r"""Multi-controlled-Phase gate.
This is a diagonal and symmetric gate that induces a
phase on the state of the target qubit, depending on the state of the control qubits.
**Circuit symbol:**
.. parsed-literal::
q_0: ───■────
│
.
│
q_(n-1): ───■────
┌──┴───┐
q_n: ┤ P(λ) ├
└──────┘
.. seealso::
:class:`~qiskit.circuit.library.standard_gates.CPhaseGate`:
The singly-controlled-version of this gate.
"""
[docs] def __init__(self, lam, num_ctrl_qubits, label=None):
"""Create new MCPhase gate."""
super().__init__('mcphase', num_ctrl_qubits + 1, [lam], num_ctrl_qubits=num_ctrl_qubits,
label=label, base_gate=PhaseGate(lam))
def _define(self):
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
q = QuantumRegister(self.num_qubits, 'q')
qc = QuantumCircuit(q, name=self.name)
if self.num_ctrl_qubits == 0:
qc.p(self.params[0], 0)
if self.num_ctrl_qubits == 1:
qc.cp(self.params[0], 0, 1)
else:
from .u3 import _gray_code_chain
scaled_lam = self.params[0] / (2 ** (self.num_ctrl_qubits - 1))
bottom_gate = CPhaseGate(scaled_lam)
definition = _gray_code_chain(q, self.num_ctrl_qubits, bottom_gate)
qc.data = definition
self.definition = qc
[docs] def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
"""Controlled version of this 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 ctrl_state is None:
gate = MCPhaseGate(self.params[0],
num_ctrl_qubits=num_ctrl_qubits + self.num_ctrl_qubits,
label=label)
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):
r"""Return inverted MCU1 gate (:math:`MCU1(\lambda){\dagger} = MCU1(-\lambda)`)"""
return MCPhaseGate(-self.params[0], self.num_ctrl_qubits)