# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2020.
#
# 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
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"""The real-amplitudes 2-local circuit."""
from __future__ import annotations
from collections.abc import Callable
import numpy as np
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library.standard_gates import RYGate, CXGate
from .two_local import TwoLocal
[docs]class RealAmplitudes(TwoLocal):
r"""The real-amplitudes 2-local circuit.
The ``RealAmplitudes`` circuit is a heuristic trial wave function used as Ansatz in chemistry
applications or classification circuits in machine learning. The circuit consists of
alternating layers of :math:`Y` rotations and :math:`CX` entanglements. The entanglement
pattern can be user-defined or selected from a predefined set.
It is called ``RealAmplitudes`` since the prepared quantum states will only have
real amplitudes, the complex part is always 0.
For example a ``RealAmplitudes`` circuit with 2 repetitions on 3 qubits with ``'reverse_linear'``
entanglement is
.. parsed-literal::
┌──────────┐ ░ ░ ┌──────────┐ ░ ░ ┌──────────┐
┤ Ry(θ[0]) ├─░────────■───░─┤ Ry(θ[3]) ├─░────────■───░─┤ Ry(θ[6]) ├
├──────────┤ ░ ┌─┴─┐ ░ ├──────────┤ ░ ┌─┴─┐ ░ ├──────────┤
┤ Ry(θ[1]) ├─░───■──┤ X ├─░─┤ Ry(θ[4]) ├─░───■──┤ X ├─░─┤ Ry(θ[7]) ├
├──────────┤ ░ ┌─┴─┐└───┘ ░ ├──────────┤ ░ ┌─┴─┐└───┘ ░ ├──────────┤
┤ Ry(θ[2]) ├─░─┤ X ├──────░─┤ Ry(θ[5]) ├─░─┤ X ├──────░─┤ Ry(θ[8]) ├
└──────────┘ ░ └───┘ ░ └──────────┘ ░ └───┘ ░ └──────────┘
The entanglement can be set using the ``entanglement`` keyword as string or a list of
index-pairs. See the documentation of :class:`~qiskit.circuit.library.TwoLocal` and
:class:`~qiskit.circuit.NLocal` for more detail. Additional options that can be set include the
number of repetitions, skipping rotation gates on qubits that are not entangled, leaving out
the final rotation layer and inserting barriers in between the rotation and entanglement
layers.
If some qubits are not entangled with other qubits it makes sense to not apply rotation gates
on these qubits, since a sequence of :math:`Y` rotations can be reduced to a single :math:`Y`
rotation with summed rotation angles.
Examples:
>>> ansatz = RealAmplitudes(3, reps=2) # create the circuit on 3 qubits
>>> print(ansatz)
┌──────────┐ ┌──────────┐ ┌──────────┐
q_0: ┤ Ry(θ[0]) ├──────────■──────┤ Ry(θ[3]) ├──────────■──────┤ Ry(θ[6]) ├
├──────────┤ ┌─┴─┐ ├──────────┤ ┌─┴─┐ ├──────────┤
q_1: ┤ Ry(θ[1]) ├──■─────┤ X ├────┤ Ry(θ[4]) ├──■─────┤ X ├────┤ Ry(θ[7]) ├
├──────────┤┌─┴─┐┌──┴───┴───┐└──────────┘┌─┴─┐┌──┴───┴───┐└──────────┘
q_2: ┤ Ry(θ[2]) ├┤ X ├┤ Ry(θ[5]) ├────────────┤ X ├┤ Ry(θ[8]) ├────────────
└──────────┘└───┘└──────────┘ └───┘└──────────┘
>>> ansatz = RealAmplitudes(3, entanglement='full', reps=2) # it is the same unitary as above
>>> print(ansatz)
┌──────────┐ ┌──────────┐ ┌──────────┐
q_0: ┤ RY(θ[0]) ├──■────■──┤ RY(θ[3]) ├──────────────■────■──┤ RY(θ[6]) ├────────────
├──────────┤┌─┴─┐ │ └──────────┘┌──────────┐┌─┴─┐ │ └──────────┘┌──────────┐
q_1: ┤ RY(θ[1]) ├┤ X ├──┼───────■──────┤ RY(θ[4]) ├┤ X ├──┼───────■──────┤ RY(θ[7]) ├
├──────────┤└───┘┌─┴─┐ ┌─┴─┐ ├──────────┤└───┘┌─┴─┐ ┌─┴─┐ ├──────────┤
q_2: ┤ RY(θ[2]) ├─────┤ X ├───┤ X ├────┤ RY(θ[5]) ├─────┤ X ├───┤ X ├────┤ RY(θ[8]) ├
└──────────┘ └───┘ └───┘ └──────────┘ └───┘ └───┘ └──────────┘
>>> ansatz = RealAmplitudes(3, entanglement='linear', reps=2, insert_barriers=True)
>>> qc = QuantumCircuit(3) # create a circuit and append the RY variational form
>>> qc.compose(ansatz, inplace=True)
>>> qc.draw()
┌──────────┐ ░ ░ ┌──────────┐ ░ ░ ┌──────────┐
q_0: ┤ RY(θ[0]) ├─░───■────────░─┤ RY(θ[3]) ├─░───■────────░─┤ RY(θ[6]) ├
├──────────┤ ░ ┌─┴─┐ ░ ├──────────┤ ░ ┌─┴─┐ ░ ├──────────┤
q_1: ┤ RY(θ[1]) ├─░─┤ X ├──■───░─┤ RY(θ[4]) ├─░─┤ X ├──■───░─┤ RY(θ[7]) ├
├──────────┤ ░ └───┘┌─┴─┐ ░ ├──────────┤ ░ └───┘┌─┴─┐ ░ ├──────────┤
q_2: ┤ RY(θ[2]) ├─░──────┤ X ├─░─┤ RY(θ[5]) ├─░──────┤ X ├─░─┤ RY(θ[8]) ├
└──────────┘ ░ └───┘ ░ └──────────┘ ░ └───┘ ░ └──────────┘
>>> ansatz = RealAmplitudes(4, reps=1, entanglement='circular', insert_barriers=True)
>>> print(ansatz)
┌──────────┐ ░ ┌───┐ ░ ┌──────────┐
q_0: ┤ RY(θ[0]) ├─░─┤ X ├──■─────────────░─┤ RY(θ[4]) ├
├──────────┤ ░ └─┬─┘┌─┴─┐ ░ ├──────────┤
q_1: ┤ RY(θ[1]) ├─░───┼──┤ X ├──■────────░─┤ RY(θ[5]) ├
├──────────┤ ░ │ └───┘┌─┴─┐ ░ ├──────────┤
q_2: ┤ RY(θ[2]) ├─░───┼───────┤ X ├──■───░─┤ RY(θ[6]) ├
├──────────┤ ░ │ └───┘┌─┴─┐ ░ ├──────────┤
q_3: ┤ RY(θ[3]) ├─░───■────────────┤ X ├─░─┤ RY(θ[7]) ├
└──────────┘ ░ └───┘ ░ └──────────┘
>>> ansatz = RealAmplitudes(4, reps=2, entanglement=[[0,3], [0,2]],
... skip_unentangled_qubits=True)
>>> print(ansatz)
┌──────────┐ ┌──────────┐ ┌──────────┐
q_0: ┤ RY(θ[0]) ├──■───────■──────┤ RY(θ[3]) ├──■───────■──────┤ RY(θ[6]) ├
└──────────┘ │ │ └──────────┘ │ │ └──────────┘
q_1: ──────────────┼───────┼────────────────────┼───────┼──────────────────
┌──────────┐ │ ┌─┴─┐ ┌──────────┐ │ ┌─┴─┐ ┌──────────┐
q_2: ┤ RY(θ[1]) ├──┼─────┤ X ├────┤ RY(θ[4]) ├──┼─────┤ X ├────┤ RY(θ[7]) ├
├──────────┤┌─┴─┐┌──┴───┴───┐└──────────┘┌─┴─┐┌──┴───┴───┐└──────────┘
q_3: ┤ RY(θ[2]) ├┤ X ├┤ RY(θ[5]) ├────────────┤ X ├┤ RY(θ[8]) ├────────────
└──────────┘└───┘└──────────┘ └───┘└──────────┘
"""
def __init__(
self,
num_qubits: int | None = None,
entanglement: str | list[list[int]] | Callable[[int], list[int]] = "reverse_linear",
reps: int = 3,
skip_unentangled_qubits: bool = False,
skip_final_rotation_layer: bool = False,
parameter_prefix: str = "θ",
insert_barriers: bool = False,
initial_state: QuantumCircuit | None = None,
name: str = "RealAmplitudes",
flatten: bool | None = None,
) -> None:
"""
Args:
num_qubits: The number of qubits of the RealAmplitudes circuit.
reps: Specifies how often the structure of a rotation layer followed by an entanglement
layer is repeated.
entanglement: Specifies the entanglement structure. Can be a string ('full', 'linear'
'reverse_linear, 'circular' or 'sca'), a list of integer-pairs specifying the indices
of qubits entangled with one another, or a callable returning such a list provided with
the index of the entanglement layer.
Default to 'reverse_linear' entanglement.
Note that 'reverse_linear' entanglement provides the same unitary as 'full'
with fewer entangling gates.
See the Examples section of :class:`~qiskit.circuit.library.TwoLocal` for more
detail.
initial_state: A `QuantumCircuit` object to prepend to the circuit.
skip_unentangled_qubits: If True, the single qubit gates are only applied to qubits
that are entangled with another qubit. If False, the single qubit gates are applied
to each qubit in the Ansatz. Defaults to False.
skip_final_rotation_layer: If False, a rotation layer is added at the end of the
ansatz. If True, no rotation layer is added.
parameter_prefix: The parameterized gates require a parameter to be defined, for which
we use :class:`~qiskit.circuit.ParameterVector`.
insert_barriers: If True, barriers are inserted in between each layer. If False,
no barriers are inserted.
flatten: Set this to ``True`` to output a flat circuit instead of nesting it inside multiple
layers of gate objects. By default currently the contents of
the output circuit will be wrapped in nested objects for
cleaner visualization. However, if you're using this circuit
for anything besides visualization its **strongly** recommended
to set this flag to ``True`` to avoid a large performance
overhead for parameter binding.
"""
super().__init__(
num_qubits=num_qubits,
reps=reps,
rotation_blocks=RYGate,
entanglement_blocks=CXGate,
entanglement=entanglement,
initial_state=initial_state,
skip_unentangled_qubits=skip_unentangled_qubits,
skip_final_rotation_layer=skip_final_rotation_layer,
parameter_prefix=parameter_prefix,
insert_barriers=insert_barriers,
name=name,
flatten=flatten,
)
@property
def parameter_bounds(self) -> list[tuple[float, float]]:
"""Return the parameter bounds.
Returns:
The parameter bounds.
"""
return self.num_parameters * [(-np.pi, np.pi)]