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.. image:: https://circleci.com/gh/dwavesystems/dwave-samplers.svg?style=svg
:target: https://circleci.com/gh/dwavesystems/dwave-samplers
.. index-start-marker
==============
dwave-samplers
==============
Ocean software provides a variety of quantum, classical, and quantum-classical
`dimod <https://docs.ocean.dwavesys.com/en/stable/docs_dimod/sdk_index.html>`_
`samplers <https://docs.ocean.dwavesys.com/en/stable/concepts/samplers.html>`_
that run either remotely (for example, in D-Wave's
`Leap <https://cloud.dwavesys.com/leap/>`_ environment) or locally on your CPU.
*dwave-samplers* implements the following classical algorithms for solving
`binary quadratic models <https://docs.ocean.dwavesys.com/en/stable/concepts/bqm.html>`_
(BQM):
* `Planar`_: an exact solver for planar Ising problems with no linear biases.
* `Random`_: a sampler that draws uniform random samples.
* `Simulated Annealing`_: a probabilistic heuristic for optimization and approximate
Boltzmann sampling well suited to finding good solutions of large problems.
* `Steepest Descent`_: a discrete analogue of gradient descent, often used in
machine learning, that quickly finds a local minimum.
* `Tabu`_: a heuristic that employs local search with methods to escape local minima.
* `Tree Decomposition`_: an exact solver for problems with low treewidth.
Planar
======
There are polynomial-time algorithms for finding the ground state of a planar
Ising model [#]_.
.. [#] Nicol Schraudolph, Dmitry Kamenetsky. *Efficient Exact Inference in Planar Ising Models*.
Advances in Neural Information Processing Systems 21 (NIPS 2008).
>>> from dwave.samplers import PlanarGraphSolver
>>> solver = PlanarGraphSolver()
Get the ground state of a planar Ising model
>>> h = {}
>>> J = {(0, 1): -1, (1, 2): -1, (0, 2): 1}
>>> sampleset = solver.sample_ising(h, J)
Random
======
Random samplers provide a useful baseline performance comparison. The variable
assignments in each sample are chosen by a coin flip.
>>> from dwave.samplers import RandomSampler
>>> sampler = RandomSampler()
Create a random binary quadratic model.
>>> import dimod
>>> bqm = dimod.generators.gnp_random_bqm(100, .5, 'BINARY')
Get the best 5 sample found in .1 seconds.
>>> sampleset = sampler.sample(bqm, time_limit=.1, max_num_samples=5)
>>> num_reads = sampleset.info['num_reads'] # the total number of samples generated
Simulated Annealing
===================
`Simulated annealing <https://en.wikipedia.org/wiki/Simulated_annealing>`__ can be
used for heuristic optimization or approximate Boltzmann sampling. The
*dwave-samplers* implementation approaches the equilibrium distribution by
performing updates at a sequence of decreasing temperatures, terminating at the
target `β`.\ [#]_ Each spin is updated once in a fixed order per point
per temperature according to a Metropolis-Hastings update. When the temperature
is low the target distribution concentrates, at equilibrium, over ground states
of the model. Samples are guaranteed to match the equilibrium for long, smooth
temperature schedules.
.. [#] `β` represents the inverse temperature, `1/(k T)`, of a
`Boltzmann distribution <https://en.wikipedia.org/wiki/Boltzmann_distribution>`_
where `T` is the thermodynamic temperature in kelvin and `k` is
Boltzmann's constant.
>>> from dwave.samplers import SimulatedAnnealingSampler
>>> sampler = SimulatedAnnealingSampler()
Create a random binary quadratic model.
>>> import dimod
>>> bqm = dimod.generators.gnp_random_bqm(100, .5, 'BINARY')
Sample using simulated annealing with both the default temperature schedule
and a custom one.
>>> sampleset = sampler.sample(bqm)
>>> sampleset = sampler.sample(bqm, beta_range=[.1, 4.2], beta_schedule_type='linear')
Steepest Descent
================
`Steepest descent <https://en.wikipedia.org/wiki/Gradient_descent>`__ is the
discrete analogue of gradient descent, but the best move is computed using a local
minimization rather rather than computing a gradient. The dimension along which
to descend is determined, at each step, by the variable flip that causes the
greatest reduction in energy.
Steepest descent is fast and effective for unfrustrated problems, but it can get
stuck in local minima.
The quadratic unconstrained binary optimization (QUBO)
`E(x, y) = x + y - 2.5 * x * y`, for example, has two local minima:
`(0, 0)` with an energy of `0` and `(1, 1)` with an energy of `-0.5`.
>>> from dwave.samplers import SteepestDescentSolver
>>> solver = SteepestDescentSolver()
Construct the QUBO:
>>> from dimod import Binaries
>>> x, y = Binaries(['x', 'y'])
>>> qubo = x + y - 2.5 * x * y
If the solver starts uphill from the global minimum, it takes the steepest path
and finds the optimal solution.
>>> sampleset = solver.sample(qubo, initial_states={'x': 0, 'y': 1})
>>> print(sampleset)
x y energy num_oc. num_st.
0 1 1 -0.5 1 1
['BINARY', 1 rows, 1 samples, 2 variables]
If the solver starts in a local minimum, it gets stuck.
>>> sampleset = solver.sample(qubo, initial_states={'x': 0, 'y': 0})
>>> print(sampleset)
x y energy num_oc. num_st.
0 0 0 0.0 1 0
['BINARY', 1 rows, 1 samples, 2 variables]
Tabu
====
`Tabu search <https://en.wikipedia.org/wiki/Tabu_search>`__ is a heuristic that
employs local search and can escape local minima by maintaining a "tabu list" of
recently explored states that it does not revisit. The length of this tabu list
is called the "tenure". *dwave-samplers* implementats the
`MST2 multistart tabu search algorithm <https://link.springer.com/article/10.1023/B:ANOR.0000039522.58036.68>`_
for quadratic unconstrained binary optimization (QUBO) problems.
Each read of the tabu algorithm consists of many starts. The solver takes the best
non-tabu step repeatedly until it does not improve its energy any more.
>>> from dwave.samplers import TabuSampler
>>> sampler = TabuSampler()
Construct a simple problem.
>>> from dimod import Binaries
>>> a, b = Binaries(['a', 'b'])
>>> qubo = -.5 * a + b - a * b
Sample using both default and custom values of tenure and number of restarts.
>>> sampleset0 = sampler.sample(qubo)
>>> sampleset1 = sampler.sample(qubo, tenure=1, num_restarts=1)
Tree Decomposition
==================
`Tree decomposition <https://en.wikipedia.org/wiki/Tree_decomposition>`__-based
solvers have a runtime that is exponential in the
`treewidth <https://en.wikipedia.org/wiki/Treewidth>`_ of the problem graph. For
problems with low treewidth, the solver can find ground states very quickly.
However, for even moderately dense problems, performance is very poor.
>>> from dwave.samplers import TreeDecompositionSolver
>>> solver = TreeDecompositionSolver()
Construct a large, tree-shaped problem.
>>> import dimod
>>> import networkx as nx
>>> tree = nx.balanced_tree(2, 5) # binary tree with a height of five
>>> bqm = dimod.BinaryQuadraticModel('SPIN')
>>> bqm.set_linear(0, .5)
>>> for u, v in tree.edges:
... bqm.set_quadratic(u, v, 1)
Because the BQM is a binary tree, it has a treewidth of 1 and can be solved exactly.
>>> sampleset = solver.sample(bqm)
>>> print(sampleset)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ... 62 energy num_oc.
0 -1 +1 +1 -1 -1 -1 -1 +1 +1 +1 +1 +1 +1 +1 +1 -1 -1 -1 ... +1 -62.5 1
['SPIN', 1 rows, 1 samples, 63 variables]
.. index-end-marker
Installation
============
To install the core package:
.. code-block:: bash
pip install dwave-samplers
License
=======
Released under the Apache License 2.0
Contributing
============
Ocean's `contributing guide <https://docs.ocean.dwavesys.com/en/stable/contributing.html>`_
has guidelines for contributing to Ocean packages.
Release Notes
-------------
**dwave-samplers** makes use of `reno <https://docs.openstack.org/reno/>`_ to manage its
release notes.
When making a contribution to **dwave-samplers** that will affect users, create a new
release note file by running
.. code-block:: bash
reno new your-short-descriptor-here
You can then edit the file created under ``releasenotes/notes/``.
Remove any sections not relevant to your changes.
Commit the file along with your changes.
Raw data
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"description": ".. image:: https://img.shields.io/pypi/v/dwave-samplers.svg\n :target: https://pypi.python.org/pypi/dwave-samplers\n\n.. image:: https://img.shields.io/pypi/pyversions/dwave-samplers.svg\n :target: https://pypi.python.org/pypi/dwave-samplers\n\n.. image:: https://codecov.io/gh/dwavesystems/dwave-samplers/branch/main/graph/badge.svg\n :target: https://codecov.io/gh/dwavesystems/dwave-samplers\n\n.. image:: https://circleci.com/gh/dwavesystems/dwave-samplers.svg?style=svg\n :target: https://circleci.com/gh/dwavesystems/dwave-samplers\n\n.. index-start-marker\n\n==============\ndwave-samplers\n==============\n\nOcean software provides a variety of quantum, classical, and quantum-classical\n`dimod <https://docs.ocean.dwavesys.com/en/stable/docs_dimod/sdk_index.html>`_\n`samplers <https://docs.ocean.dwavesys.com/en/stable/concepts/samplers.html>`_\nthat run either remotely (for example, in D-Wave's\n`Leap <https://cloud.dwavesys.com/leap/>`_ environment) or locally on your CPU.\n\n*dwave-samplers* implements the following classical algorithms for solving\n`binary quadratic models <https://docs.ocean.dwavesys.com/en/stable/concepts/bqm.html>`_\n(BQM):\n\n* `Planar`_: an exact solver for planar Ising problems with no linear biases.\n* `Random`_: a sampler that draws uniform random samples.\n* `Simulated Annealing`_: a probabilistic heuristic for optimization and approximate\n Boltzmann sampling well suited to finding good solutions of large problems.\n* `Steepest Descent`_: a discrete analogue of gradient descent, often used in\n machine learning, that quickly finds a local minimum.\n* `Tabu`_: a heuristic that employs local search with methods to escape local minima.\n* `Tree Decomposition`_: an exact solver for problems with low treewidth.\n\nPlanar\n======\n\nThere are polynomial-time algorithms for finding the ground state of a planar\nIsing model [#]_.\n\n.. [#] Nicol Schraudolph, Dmitry Kamenetsky. *Efficient Exact Inference in Planar Ising Models*.\n Advances in Neural Information Processing Systems 21 (NIPS 2008).\n\n>>> from dwave.samplers import PlanarGraphSolver\n>>> solver = PlanarGraphSolver()\n\nGet the ground state of a planar Ising model\n\n>>> h = {}\n>>> J = {(0, 1): -1, (1, 2): -1, (0, 2): 1}\n\n>>> sampleset = solver.sample_ising(h, J)\n\nRandom\n======\n\nRandom samplers provide a useful baseline performance comparison. The variable\nassignments in each sample are chosen by a coin flip.\n\n>>> from dwave.samplers import RandomSampler\n>>> sampler = RandomSampler()\n\nCreate a random binary quadratic model.\n\n>>> import dimod\n>>> bqm = dimod.generators.gnp_random_bqm(100, .5, 'BINARY')\n\nGet the best 5 sample found in .1 seconds.\n\n>>> sampleset = sampler.sample(bqm, time_limit=.1, max_num_samples=5)\n>>> num_reads = sampleset.info['num_reads'] # the total number of samples generated\n\nSimulated Annealing\n===================\n\n`Simulated annealing <https://en.wikipedia.org/wiki/Simulated_annealing>`__ can be\nused for heuristic optimization or approximate Boltzmann sampling. The\n*dwave-samplers* implementation approaches the equilibrium distribution by\nperforming updates at a sequence of decreasing temperatures, terminating at the\ntarget `\u03b2`.\\ [#]_ Each spin is updated once in a fixed order per point\nper temperature according to a Metropolis-Hastings update. When the temperature\nis low the target distribution concentrates, at equilibrium, over ground states\nof the model. Samples are guaranteed to match the equilibrium for long, smooth\ntemperature schedules.\n\n.. [#] `\u03b2` represents the inverse temperature, `1/(k T)`, of a\n `Boltzmann distribution <https://en.wikipedia.org/wiki/Boltzmann_distribution>`_\n where `T` is the thermodynamic temperature in kelvin and `k` is\n Boltzmann's constant.\n\n>>> from dwave.samplers import SimulatedAnnealingSampler\n>>> sampler = SimulatedAnnealingSampler()\n\nCreate a random binary quadratic model.\n\n>>> import dimod\n>>> bqm = dimod.generators.gnp_random_bqm(100, .5, 'BINARY')\n\nSample using simulated annealing with both the default temperature schedule\nand a custom one.\n\n>>> sampleset = sampler.sample(bqm)\n>>> sampleset = sampler.sample(bqm, beta_range=[.1, 4.2], beta_schedule_type='linear')\n\nSteepest Descent\n================\n\n`Steepest descent <https://en.wikipedia.org/wiki/Gradient_descent>`__ is the\ndiscrete analogue of gradient descent, but the best move is computed using a local\nminimization rather rather than computing a gradient. 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