Package: dwave-samplers
dwave-samplersOcean software provides a variety of quantum, classical, and quantum-classicaldimodsamplersthat run either remotely (for example, in D-Wave’sLeapenvironment) or locally on your CPU.dwave-samplersimplements the following classical algorithms for solvingbinary quadratic models(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.PlanarThere are polynomial-time algorithms for finding the ground state of a planar
Ising model[1].[1]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)RandomRandom 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 generatedSimulated AnnealingSimulated annealingcan be
used for heuristic optimization or approximate Boltzmann sampling. Thedwave-samplersimplementation approaches the equilibrium distribution by
performing updates at a sequence of decreasing temperatures, terminating at the
targetβ.[2]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.[2]βrepresents the inverse temperature,1/(k T), of aBoltzmann distributionwhereTis the thermodynamic temperature in kelvin andkis
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 DescentSteepest descentis 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 of0and(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 * yIf 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]TabuTabu searchis 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-samplersimplementats theMST2 multistart tabu search algorithmfor 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 * bSample 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 DecompositionTree decomposition-based
solvers have a runtime that is exponential in thetreewidthof 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]InstallationTo install the core package:pipinstalldwave-samplersLicenseReleased under the Apache License 2.0ContributingOcean’scontributing guidehas guidelines for contributing to Ocean packages.Release Notesdwave-samplersmakes use ofrenoto manage its
release notes.When making a contribution todwave-samplersthat will affect users, create a new
release note file by runningrenonewyour-short-descriptor-hereYou can then edit the file created underreleasenotes/notes/.
Remove any sections not relevant to your changes.
Commit the file along with your changes.