PyQUBO allows you to create QUBOs or Ising models from flexible mathematical expressions easily. Some of the features of PyQUBO are

  • Python based (C++ backend).
  • Fully integrated with Ocean SDK. (details)
  • Automatic validation of constraints. (details)
  • Placeholder for parameter tuning. (details)

For more details, see PyQUBO Documentation.

Example Usage

Creating QUBO

This example constructs a simple expression and compile it to model. By calling model.to_qubo(), we get the resulting QUBO. (This example solves Number Partitioning Problem with a set S = {4, 2, 7, 1})

>>> from pyqubo import Spin
>>> s1, s2, s3, s4 = Spin("s1"), Spin("s2"), Spin("s3"), Spin("s4")
>>> H = (4*s1 + 2*s2 + 7*s3 + s4)**2
>>> model = H.compile()
>>> qubo, offset = model.to_qubo()
>>> pprint(qubo)
{('s1', 's1'): -160.0,
('s1', 's2'): 64.0,
('s2', 's2'): -96.0,
('s3', 's1'): 224.0,
('s3', 's2'): 112.0,
('s3', 's3'): -196.0,
('s4', 's1'): 32.0,
('s4', 's2'): 16.0,
('s4', 's3'): 56.0,
('s4', 's4'): -52.0}

Integration with D-Wave Ocean

PyQUBO can output the BinaryQuadraticModel(BQM) which is compatible with Sampler class defined in D-Wave Ocean SDK. In the example below, we solve the problem with SimulatedAnnealingSampler.

>>> import neal
>>> sampler = neal.SimulatedAnnealingSampler()
>>> bqm = model.to_bqm()
>>> sampleset = sampler.sample(bqm, num_reads=10)
>>> decoded_samples = model.decode_sampleset(sampleset)
>>> best_sample = min(decoded_samples, key=lambda x:
>>> best_sample.sample # doctest: +SKIP
{'s1': 0, 's2': 0, 's3': 1, 's4': 0}

If you want to solve the problem by actual D-Wave machines, just replace the sampler by a DWaveCliqueSampler instance, for example.

For more examples, see example notebooks.


Since the core logic of the new PyQUBO (>=1.0.0) is written in C++ and the logic itself is also optimized, the execution time to produce QUBO has become shorter. We benchmarked the execution time to produce QUBOs of TSP with the new PyQUBO (1.0.0) and the previous PyQUBO (0.4.0). The result shows the new PyQUBO runs 1000 times faster as the problem size increases.

Execution time includes building Hamiltonian, compilation, and producing QUBOs. The code to produce the above result is found in here.


pip install pyqubo


python install

Supported Python Versions

Python 3.5, 3.6, 3.7, 3.8 and 3.9 are supported.

Supported Operating Systems

  • Linux (32/64bit)
  • OSX (64bit, >=10.9)
  • Win (64bit)

Indices and tables