Source code for pennylane.templates.subroutines.out_multiplier
# Copyright 2018-2024 Xanadu Quantum Technologies Inc.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
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# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Contains the OutMultiplier template.
"""
import pennylane as qml
from pennylane.operation import Operation
[docs]class OutMultiplier(Operation):
r"""Performs the out-place modular multiplication operation.
This operator performs the modular multiplication of integers :math:`x` and :math:`y` modulo
:math:`mod` in the computational basis:
.. math::
\text{OutMultiplier}(mod) |x \rangle |y \rangle |b \rangle = |x \rangle |y \rangle |b + x \cdot y \; \text{mod} \; mod \rangle,
The implementation is based on the quantum Fourier transform method presented in
`arXiv:2311.08555 <https://arxiv.org/abs/2311.08555>`_.
.. note::
To obtain the correct result, :math:`x`, :math:`y` and :math:`b` must be smaller than :math:`mod`.
.. seealso:: :class:`~.PhaseAdder` and :class:`~.Multiplier`.
Args:
x_wires (Sequence[int]): the wires that store the integer :math:`x`
y_wires (Sequence[int]): the wires that store the integer :math:`y`
output_wires (Sequence[int]): the wires that store the multiplication result. If the register is in a non-zero state :math:`b`, the solution will be added to this value
mod (int): the modulo for performing the multiplication. If not provided, it will be set to its maximum value, :math:`2^{\text{len(output_wires)}}`
work_wires (Sequence[int]): the auxiliary wires to use for the multiplication. The
work wires are not needed if :math:`mod=2^{\text{len(output_wires)}}`, otherwise two work wires
should be provided. Defaults to ``None``.
**Example**
This example performs the multiplication of two integers :math:`x=2` and :math:`y=7` modulo :math:`mod=12`.
We'll let :math:`b=0`. See Usage Details for :math:`b \neq 0`.
.. code-block::
x = 2
y = 7
mod = 12
x_wires = [0, 1]
y_wires = [2, 3, 4]
output_wires = [6, 7, 8, 9]
work_wires = [5, 10]
dev = qml.device("default.qubit", shots=1)
@qml.qnode(dev)
def circuit():
qml.BasisEmbedding(x, wires=x_wires)
qml.BasisEmbedding(y, wires=y_wires)
qml.OutMultiplier(x_wires, y_wires, output_wires, mod, work_wires)
return qml.sample(wires=output_wires)
.. code-block:: pycon
>>> print(circuit())
[0 0 1 0]
The result :math:`[0 0 1 0]`, is the binary representation of
:math:`2 \cdot 7 \; \text{modulo} \; 12 = 2`.
.. details::
:title: Usage Details
This template takes as input four different sets of wires.
The first one is ``x_wires`` which is used
to encode the integer :math:`x < mod` in the computational basis. Therefore, ``x_wires`` must contain
at least :math:`\lceil \log_2(x)\rceil` wires to represent :math:`x`.
The second one is ``y_wires`` which is used
to encode the integer :math:`y < mod` in the computational basis. Therefore, ``y_wires`` must contain
at least :math:`\lceil \log_2(y)\rceil` wires to represent :math:`y`.
The third one is ``output_wires`` which is used
to encode the integer :math:`b+ x \cdot y \; \text{mod} \; mod` in the computational basis. Therefore, it will require at least
:math:`\lceil \log_2(mod)\rceil` ``output_wires`` to represent :math:`b + x \cdot y \; \text{mod} \; mod`. Note that these wires can be initialized with any integer
:math:`b < mod`, but the most common choice is :math:`b=0` to obtain as a final result :math:`x \cdot y \; \text{mod} \; mod`.
The following is an example for :math:`b = 1`.
.. code-block::
b = 1
x = 2
y = 7
mod = 12
x_wires = [0, 1]
y_wires = [2, 3, 4]
output_wires = [6, 7, 8, 9]
work_wires = [5, 10]
dev = qml.device("default.qubit", shots=1)
@qml.qnode(dev)
def circuit():
qml.BasisEmbedding(x, wires=x_wires)
qml.BasisEmbedding(y, wires=y_wires)
qml.BasisEmbedding(b, wires=output_wires)
qml.OutMultiplier(x_wires, y_wires, output_wires, mod, work_wires)
return qml.sample(wires=output_wires)
.. code-block:: pycon
>>> print(circuit())
[0 0 1 1]
The result :math:`[0 0 1 1]`, is the binary representation of
:math:`2 \cdot 7 + 1\; \text{modulo} \; 12 = 3`.
The fourth set of wires is ``work_wires`` which consist of the auxiliary qubits used to perform the modular multiplication operation.
- If :math:`mod = 2^{\text{len(output_wires)}}`, there will be no need for ``work_wires``, hence ``work_wires=None``. This is the case by default.
- If :math:`mod \neq 2^{\text{len(output_wires)}}`, two ``work_wires`` have to be provided.
Note that the ``OutMultiplier`` template allows us to perform modular multiplication in the computational basis. However if one just wants to perform
standard multiplication (with no modulo), that would be equivalent to setting the modulo :math:`mod` to a large enough value to ensure that :math:`x \cdot k < mod`.
"""
grad_method = None
def __init__(
self, x_wires, y_wires, output_wires, mod=None, work_wires=None, id=None
): # pylint: disable=too-many-arguments
x_wires = qml.wires.Wires(x_wires)
y_wires = qml.wires.Wires(y_wires)
output_wires = qml.wires.Wires(output_wires)
num_work_wires = 0 if work_wires is None else len(work_wires)
if mod is None:
mod = 2 ** len(output_wires)
if mod != 2 ** len(output_wires) and num_work_wires != 2:
raise ValueError(
f"If mod is not 2^{len(output_wires)}, two work wires should be provided."
)
if mod > 2 ** (len(output_wires)):
raise ValueError(
"OutMultiplier must have enough wires to represent mod. The maximum mod "
f"with len(output_wires)={len(output_wires)} is {2 ** len(output_wires)}, but received {mod}."
)
if work_wires is not None:
if any(wire in work_wires for wire in x_wires):
raise ValueError("None of the wires in work_wires should be included in x_wires.")
if any(wire in work_wires for wire in y_wires):
raise ValueError("None of the wires in work_wires should be included in y_wires.")
if any(wire in y_wires for wire in x_wires):
raise ValueError("None of the wires in y_wires should be included in x_wires.")
if any(wire in x_wires for wire in output_wires):
raise ValueError("None of the wires in x_wires should be included in output_wires.")
if any(wire in y_wires for wire in output_wires):
raise ValueError("None of the wires in y_wires should be included in output_wires.")
wires_list = [x_wires, y_wires, output_wires]
wires_name = ["x_wires", "y_wires", "output_wires"]
self.hyperparameters["work_wires"] = work_wires
if work_wires is not None:
wires_list.append(work_wires)
wires_name.append("work_wires")
for name, wires in zip(wires_name, wires_list):
self.hyperparameters[name] = qml.wires.Wires(wires)
self.hyperparameters["mod"] = mod
# pylint: disable=consider-using-generator
all_wires = sum([self.hyperparameters[name] for name in wires_name], start=[])
super().__init__(wires=all_wires, id=id)
@property
def num_params(self):
return 0
def _flatten(self):
metadata = tuple((key, value) for key, value in self.hyperparameters.items())
return tuple(), metadata
@classmethod
def _unflatten(cls, data, metadata):
hyperparams_dict = dict(metadata)
return cls(**hyperparams_dict)
[docs] def map_wires(self, wire_map: dict):
new_dict = {
key: [wire_map.get(w, w) for w in self.hyperparameters[key]]
for key in ["x_wires", "y_wires", "output_wires", "work_wires"]
}
return OutMultiplier(
new_dict["x_wires"],
new_dict["y_wires"],
new_dict["output_wires"],
self.hyperparameters["mod"],
new_dict["work_wires"],
)
[docs] def decomposition(self): # pylint: disable=arguments-differ
return self.compute_decomposition(**self.hyperparameters)
@classmethod
def _primitive_bind_call(cls, *args, **kwargs):
return cls._primitive.bind(*args, **kwargs)
[docs] @staticmethod
def compute_decomposition(
x_wires, y_wires, output_wires, mod, work_wires
): # pylint: disable=arguments-differ
r"""Representation of the operator as a product of other operators.
Args:
x_wires (Sequence[int]): the wires that store the integer :math:`x`
y_wires (Sequence[int]): the wires that store the integer :math:`y`
output_wires (Sequence[int]): the wires that store the multiplication result. If the register is in a non-zero state :math:`b`, the solution will be added to this value
mod (int): the modulo for performing the multiplication. If not provided, it will be set to its maximum value, :math:`2^{\text{len(output_wires)}}`
work_wires (Sequence[int]): the auxiliary wires to use for the multiplication. The
work wires are not needed if :math:`mod=2^{\text{len(output_wires)}}`, otherwise two work wires
should be provided. Defaults to ``None``.
Returns:
list[.Operator]: Decomposition of the operator
**Example**
>>> qml.OutMultiplier.compute_decomposition(x_wires=[0,1], y_wires=[2,3], output_wires=[5,6], mod=4, work_wires=[4,7])
[QFT(wires=[5, 6]),
ControlledSequence(ControlledSequence(PhaseAdder(wires=[5, 6]), control=[0, 1]), control=[2, 3]),
Adjoint(QFT(wires=[5, 6]))]
"""
op_list = []
if mod != 2 ** len(output_wires):
qft_output_wires = work_wires[:1] + output_wires
work_wire = work_wires[1:]
else:
qft_output_wires = output_wires
work_wire = None
op_list.append(qml.QFT(wires=qft_output_wires))
op_list.append(
qml.ControlledSequence(
qml.ControlledSequence(
qml.PhaseAdder(1, qft_output_wires, mod, work_wire), control=x_wires
),
control=y_wires,
)
)
op_list.append(qml.adjoint(qml.QFT)(wires=qft_output_wires))
return op_list
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