/
integer.py
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/
integer.py
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# Copyright 2021 D-Wave Systems 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
#
# Unless required by applicable law or agreed to in writing, software
# 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.
import math
from dimod.binary.binary_quadratic_model import BinaryQuadraticModel
from dimod.typing import Variable
from dimod.vartypes import Vartype
__all__ = ['binary_encoding']
def binary_encoding(v: Variable, upper_bound: int) -> BinaryQuadraticModel:
"""Generate a binary quadratic model encoding an integer.
Args:
v: Integer variable label.
upper_bound: Upper bound on the integer value (inclusive). You can set
a lower bound by setting the model's offset.
Returns:
A binary quadratic model. Variables in the BQM are labelled with tuples
with the following two or three values: first, the specified variable
label, ``v``; second, the coefficient in the integer encoding; third
(only in the tuple representing the most significant bit), a string,
``'msb'``.
Example:
>>> bqm = dimod.generators.binary_encoding('i', 6)
>>> bqm
BinaryQuadraticModel({('i', 1): 1.0, ('i', 2): 2.0, ('i', 3, 'msb'): 3.0}, {}, 0.0, 'BINARY')
You can use a sample to restore the original integer value.
>>> sample = {('i', 1): 1, ('i', 2): 0, ('i', 3, 'msb'): 1}
>>> bqm.energy(sample)
4.0
>>> sum(v[1]*val for v, val in sample.items()) + bqm.offset
4.0
If you wish to encode integers with a lower bound, you can use the
binary quadratic model's :attr:`~dimod.binary.BinaryQuadraticModel.offset`
attribute.
>>> i = dimod.generators.binary_encoding('i', 10) + 5 # integer in [5, 15]
References:
[1]: Sahar Karimi, Pooya Ronagh (2017), Practical Integer-to-Binary
Mapping for Quantum Annealers. arxiv.org:1706.01945.
"""
# note: the paper above also gives a nice way to handle bounded coefficients
# if we want to do that in the future.
if upper_bound < 2:
raise ValueError("upper_bound must be greater than or equal to 2, "
f"received {upper_bound}")
upper_bound = math.floor(upper_bound)
bqm = BinaryQuadraticModel(Vartype.BINARY)
max_pow = math.floor(math.log2(upper_bound))
for exp in range(max_pow):
val = 1 << exp
bqm.set_linear((v, val), val)
else:
val = upper_bound - ((1 << max_pow) - 1)
bqm.set_linear((v, val, 'msb'), val)
return bqm