# Source code for dwave.system.composites.tiling

```
# Copyright 2018 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.
"""
A :std:doc:`dimod composite <oceandocs:docs_dimod/reference/samplers>` that tiles small problems
multiple times to a Chimera-structured sampler.
The :class:`.TilingComposite` takes a problem that can fit on a small
:term:`Chimera` graph and replicates it across a larger
Chimera graph to obtain samples from multiple areas of the solver in one call.
For example, a 2x2 Chimera lattice could be tiled 64 times (8x8) on a fully-yielded
D-Wave 2000Q system (16x16).
See `Ocean Glossary <https://docs.ocean.dwavesys.com/en/stable/concepts/index.html>`_
for explanations of technical terms in descriptions of Ocean tools.
"""
from math import sqrt, ceil
import dimod
import dwave_networkx as dnx
import numpy as np
import dwave.embedding
__all__ = ['TilingComposite']
[docs]class TilingComposite(dimod.Sampler, dimod.Composite, dimod.Structured):
"""Composite to tile a small problem across a Chimera-structured sampler.
Enables parallel sampling for small problems (problems that are minor-embeddable in
a small part of a D-Wave solver's :term:`Chimera` graph).
Notation *CN* refers to a Chimera graph consisting of an NxN grid of unit cells, where
each unit cell is a bipartite graph with shores of size t. The D-Wave 2000Q QPU
supports a C16 Chimera graph: its 2048 qubits are logically mapped into a 16x16 matrix of
unit cell of 8 qubits (t=4).
A problem that can be minor-embedded in a single unit cell, for example, can therefore
be tiled across the unit cells of a D-Wave 2000Q as 16x16 duplicates. This enables
sampling 256 solutions in a single call.
Args:
sampler (:class:`dimod.Sampler`): Structured dimod sampler such as a :class:`~dwave.system.samplers.DWaveSampler()`.
sub_m (int): Number of rows of Chimera unit cells for minor-embedding the problem once.
sub_n (int): Number of columns of Chimera unit cells for minor-embedding the problem once.
t (int, optional, default=4): Size of the shore within each Chimera unit cell.
Examples:
This example submits a two-variable QUBO problem representing a logical
NOT gate to a D-Wave system. The QUBO---two nodes with biases of -1 that
are coupled with strength 2---needs only any two coupled qubits and so is
easily minor-embedded in a single unit cell.
Composite :class:`.TilingComposite` tiles it multiple times for parallel solution:
the two nodes should typically have opposite values.
>>> from dwave.system import DWaveSampler, EmbeddingComposite
>>> from dwave.system import TilingComposite
...
>>> qpu_2000q = DWaveSampler(solver={'topology__type': 'chimera'})
>>> sampler = EmbeddingComposite(TilingComposite(qpu_2000q, 1, 1, 4))
>>> Q = {(1, 1): -1, (1, 2): 2, (2, 1): 0, (2, 2): -1}
>>> sampleset = sampler.sample_qubo(Q)
>>> len(sampleset)> 1
True
See `Ocean Glossary <https://docs.ocean.dwavesys.com/en/stable/concepts/index.html>`_
for explanations of technical terms in descriptions of Ocean tools.
"""
nodelist = None
"""list: List of active qubits for the structured solver."""
edgelist = None
"""list: List of active couplers for the D-Wave solver."""
parameters = None
"""dict[str, list]: Parameters in the form of a dict."""
properties = None
"""dict: Properties in the form of a dict."""
children = None
"""list: The single wrapped structured sampler."""
def __init__(self, sampler, sub_m, sub_n, t=4):
self.parameters = sampler.parameters.copy()
self.properties = properties = {'child_properties': sampler.properties}
tile = dnx.chimera_graph(sub_m, sub_n, t)
self.nodelist = sorted(tile.nodes)
self.edgelist = sorted(sorted(edge) for edge in tile.edges)
# dimod.Structured abstract base class automatically populates adjacency and structure as
# mixins based on nodelist and edgelist
if not isinstance(sampler, dimod.Structured):
# we could also just tile onto the unstructured sampler but in that case we would need
# to know how many tiles to use
raise ValueError("given child sampler should be structured")
self.children = [sampler]
nodes_per_cell = t * 2
edges_per_cell = t * t
m = n = int(ceil(sqrt(ceil(len(sampler.structure.nodelist) / nodes_per_cell)))) # assume square lattice shape
system = dnx.chimera_graph(m, n, t, node_list=sampler.structure.nodelist, edge_list=sampler.structure.edgelist)
c2i = {chimera_index: linear_index for (linear_index, chimera_index) in system.nodes(data='chimera_index')}
sub_c2i = {chimera_index: linear_index for (linear_index, chimera_index) in tile.nodes(data='chimera_index')}
# Count the connections between these qubits
def _between(qubits1, qubits2):
edges = [edge for edge in system.edges if edge[0] in qubits1 and edge[1] in qubits2]
return len(edges)
# Get the list of qubits in a cell
def _cell_qubits(i, j):
return [c2i[(i, j, u, k)] for u in range(2) for k in range(t) if (i, j, u, k) in c2i]
# get a mask of complete cells
cells = [[False for _ in range(n)] for _ in range(m)]
for i in range(m):
for j in range(n):
qubits = _cell_qubits(i, j)
cells[i][j] = len(qubits) == nodes_per_cell and _between(qubits, qubits) == edges_per_cell
# List of 'embeddings'
self.embeddings = properties['embeddings'] = embeddings = []
# For each possible chimera cell check if the next few cells are complete
for i in range(m + 1 - sub_m):
for j in range(n + 1 - sub_n):
# Check if the sub cells are matched
match = all(cells[i + sub_i][j + sub_j] for sub_i in range(sub_m) for sub_j in range(sub_n))
# Check if there are connections between the cells.
for sub_i in range(sub_m):
for sub_j in range(sub_n):
if sub_m > 1 and sub_i < sub_m - 1:
match &= _between(_cell_qubits(i + sub_i, j + sub_j),
_cell_qubits(i + sub_i + 1, j + sub_j)) == t
if sub_n > 1 and sub_j < sub_n - 1:
match &= _between(_cell_qubits(i + sub_i, j + sub_j),
_cell_qubits(i + sub_i, j + sub_j + 1)) == t
if match:
# Pull those cells out into an embedding.
embedding = {}
for sub_i in range(sub_m):
for sub_j in range(sub_n):
cells[i + sub_i][j + sub_j] = False # Mark cell as matched
for u in range(2):
for k in range(t):
embedding[sub_c2i[sub_i, sub_j, u, k]] = {c2i[(i + sub_i, j + sub_j, u, k)]}
embeddings.append(embedding)
if len(embeddings) == 0:
raise ValueError("no tile embeddings found; is the sampler Chimera structured?")
[docs] @dimod.bqm_structured
def sample(self, bqm, **kwargs):
"""Sample from the specified binary quadratic model.
Args:
bqm (:obj:`dimod.BinaryQuadraticModel`):
Binary quadratic model to be sampled from.
**kwargs:
Optional keyword arguments for the sampling method, specified per solver.
Returns:
:class:`dimod.SampleSet`
Examples:
This example submits a simple Ising problem of just two variables on a
D-Wave system.
Because the problem fits in a single :term:`Chimera` unit cell, it is tiled
across the solver's entire Chimera graph, resulting in multiple samples
(the exact number depends on the working Chimera graph of the D-Wave system).
>>> from dwave.system import DWaveSampler, EmbeddingComposite
>>> from dwave.system import TilingComposite
...
>>> qpu_2000q = DWaveSampler(solver={'topology__type': 'chimera'})
>>> sampler = EmbeddingComposite(TilingComposite(qpu_2000q, 1, 1, 4))
>>> response = sampler.sample_ising({},{('a', 'b'): 1})
>>> len(response) # doctest: +SKIP
246
See `Ocean Glossary <https://docs.ocean.dwavesys.com/en/stable/concepts/index.html>`_
for explanations of technical terms in descriptions of Ocean tools.
"""
# apply the embeddings to the given problem to tile it across the child sampler
embedded_bqm = dimod.BinaryQuadraticModel.empty(bqm.vartype)
__, __, target_adjacency = self.child.structure
for embedding in self.embeddings:
embedded_bqm.update(dwave.embedding.embed_bqm(bqm, embedding, target_adjacency))
# solve the problem on the child system
tiled_response = self.child.sample(embedded_bqm, **kwargs)
responses = []
for embedding in self.embeddings:
embedding = {v: chain for v, chain in embedding.items() if v in bqm.variables}
responses.append(dwave.embedding.unembed_sampleset(tiled_response, embedding, bqm))
answer = dimod.concatenate(responses)
answer.info.update(tiled_response.info)
return answer
@property
def num_tiles(self):
return len(self.embeddings)
```