# 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."""
from cmath import exp
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.parameterexpression import ParameterValueType
[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).
Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
with the :meth:`~qiskit.circuit.QuantumCircuit.p` method.
**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>`_
"""
def __init__(self, theta: ParameterValueType, label: Optional[str] = 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: int = 1,
label: Optional[str] = None,
ctrl_state: Optional[Union[int, str]] = None,
):
"""Return a (multi-)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])
def __array__(self, dtype=None):
"""Return a numpy.array for the Phase gate."""
lam = float(self.params[0])
return numpy.array([[1, 0], [0, exp(1j * lam)]], dtype=dtype)
[docs] def power(self, exponent: float):
"""Raise gate to a power."""
(theta,) = self.params
return PhaseGate(exponent * theta)
[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.
Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
with the :meth:`~qiskit.circuit.QuantumCircuit.cp` method.
**Circuit symbol:**
.. parsed-literal::
q_0: ─■──
│λ
q_1: ─■──
**Matrix representation:**
.. math::
CPhase =
I \otimes |0\rangle\langle 0| + P \otimes |1\rangle\langle 1| =
\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.
"""
def __init__(
self,
theta: ParameterValueType,
label: Optional[str] = None,
ctrl_state: Optional[Union[str, int]] = 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_0: ┤ P(λ/2) ├──■───────────────■────────────
# └────────┘┌─┴─┐┌─────────┐┌─┴─┐┌────────┐
# q_1: ──────────┤ X ├┤ P(-λ/2) ├┤ X ├┤ P(λ/2) ├
# └───┘└─────────┘└───┘└────────┘
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: int = 1,
label: Optional[str] = None,
ctrl_state: Optional[Union[str, int]] = 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)
def __array__(self, dtype=None):
"""Return a numpy.array for the CPhase gate."""
eith = 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=dtype
)
return numpy.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, eith, 0], [0, 0, 0, 1]], dtype=dtype)
[docs] def power(self, exponent: float):
"""Raise gate to a power."""
(theta,) = self.params
return CPhaseGate(exponent * theta)
[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.
Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
with the :meth:`~qiskit.circuit.QuantumCircuit.mcp` method.
**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.
"""
def __init__(self, lam: ParameterValueType, num_ctrl_qubits: int, label: Optional[str] = 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)
for operation, qubits, clbits in _gray_code_chain(q, self.num_ctrl_qubits, bottom_gate):
qc._append(operation, qubits, clbits)
self.definition = qc
[docs] def control(
self,
num_ctrl_qubits: int = 1,
label: Optional[str] = None,
ctrl_state: Optional[Union[str, int]] = 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)