French
Languages
English
Bengali
French
German
Japanese
Korean
Portuguese
Spanish
Tamil

# Code source de qiskit.circuit.library.standard_gates.p

# This code is part of Qiskit.
#
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# 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 __future__ import annotations
from cmath import exp
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: str | None = 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), )
self.definition = qc

[docs]    def control(
self,
num_ctrl_qubits: int = 1,
label: str | None = None,
ctrl_state: str | int | None = 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, label=label, ctrl_state=ctrl_state)
elif ctrl_state is None and num_ctrl_qubits > 1:
gate = MCPhaseGate(self.params, 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)

def __array__(self, dtype=None):
"""Return a numpy.array for the Phase gate."""
lam = float(self.params)
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: str | None = None,
ctrl_state: str | int | None = 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 / 2, 0)
qc.cx(0, 1)
qc.p(-self.params / 2, 1)
qc.cx(0, 1)
qc.p(self.params / 2, 1)
self.definition = qc

[docs]    def control(
self,
num_ctrl_qubits: int = 1,
label: str | None = None,
ctrl_state: str | int | None = 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, 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, ctrl_state=self.ctrl_state)

def __array__(self, dtype=None):
"""Return a numpy.array for the CPhase gate."""
eith = exp(1j * float(self.params))
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: str | None = 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)
if self.num_ctrl_qubits == 1:
qc.cp(self.params, 0, 1)
else:
from .u3 import _gray_code_chain

scaled_lam = self.params / (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: str | None = None,
ctrl_state: str | int | None = 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, 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, self.num_ctrl_qubits)