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Quantum Optimization
https://github.com/qiskit-community/qiskit-optimization

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Quantum Optimization

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README 

        
# Qiskit Optimization



[![License](https://img.shields.io/github/license/Qiskit/qiskit-optimization.svg?style=popout-square)](https://opensource.org/licenses/Apache-2.0)[![Build Status](https://github.com/qiskit-community/qiskit-optimization/workflows/Optimization%20Unit%20Tests/badge.svg?branch=main)](https://github.com/qiskit-community/qiskit-optimization/actions?query=workflow%3A"Optimization%20Unit%20Tests"+branch%3Amain+event%3Apush)[![](https://img.shields.io/github/release/Qiskit/qiskit-optimization.svg?style=popout-square)](https://github.com/qiskit-community/qiskit-optimization/releases)[![](https://img.shields.io/pypi/dm/qiskit-optimization.svg?style=popout-square)](https://pypi.org/project/qiskit-optimization/)[![Coverage Status](https://coveralls.io/repos/github/Qiskit/qiskit-optimization/badge.svg?branch=main)](https://coveralls.io/github/Qiskit/qiskit-optimization?branch=main)



**Qiskit Optimization** is an open-source framework that covers the whole range from high-level modeling of optimization

problems, with automatic conversion of problems to different required representations, to a suite

of easy-to-use quantum optimization algorithms that are ready to run on classical simulators,

as well as on real quantum devices via Qiskit.



The Optimization module enables easy, efficient modeling of optimization problems using

[docplex](https://ibmdecisionoptimization.github.io/docplex-doc/).

A uniform interface as well as automatic conversion between different problem representations

allows users to solve problems using a large set of algorithms, from variational quantum algorithms,

such as the Quantum Approximate Optimization Algorithm QAOA, to Grover Adaptive Search using the

GroverOptimizer, leveraging fundamental algorithms provided by

[Qiskit Algorithms](https://qiskit-community.github.io/qiskit-algorithms/). Furthermore, the modular design

of the optimization module allows it to be easily extended and facilitates rapid development and

testing of new algorithms. Compatible classical optimizers are also provided for testing,

validation, and benchmarking.



## Installation



We encourage installing Qiskit Optimization via the pip tool (a python package manager).



```bash

pip install qiskit-optimization

```



**pip** will handle all dependencies automatically and you will always install the latest

(and well-tested) version.



If you want to work on the very latest work-in-progress versions, either to try features ahead of

their official release or if you want to contribute to Optimization, then you can install from source.

To do this follow the instructions in the

 [documentation](https://qiskit-community.github.io/qiskit-optimization/getting_started.html#installation).



----------------------------------------------------------------------------------------------------



### Optional Installs



* **IBM CPLEX** may be installed using `pip install 'qiskit-optimization[cplex]'` to enable the reading of `LP` files and the usage of

  the `CplexOptimizer`, wrapper for ``cplex.Cplex``. CPLEX is a separate package and its support of Python versions is independent of Qiskit Optimization, where this CPLEX command will have no effect if there is no compatible version of CPLEX available (yet).



* **CVXPY** may be installed using the command `pip install 'qiskit-optimization[cvx]'`.

  CVXPY being installed will enable the usage of the Goemans-Williamson algorithm as an optimizer `GoemansWilliamsonOptimizer`.



* **Matplotlib** may be installed using the command `pip install 'qiskit-optimization[matplotlib]'`.

  Matplotlib being installed will enable the usage of the `draw` method in the graph optimization application classes.



* **Gurobipy** may be installed using the command `pip install 'qiskit-optimization[gurobi]'`.

  Gurobipy being installed will enable the usage of the GurobiOptimizer.



### Creating Your First Optimization Programming Experiment in Qiskit



Now that Qiskit Optimization is installed, it's time to begin working with the optimization module.

Let's try an optimization experiment to compute the solution of a

[Max-Cut](https://en.wikipedia.org/wiki/Maximum_cut). The Max-Cut problem can be formulated as

quadratic program, which can be solved using many several different algorithms in Qiskit.

In this example, the MinimumEigenOptimizer

is employed in combination with the Quantum Approximate Optimization Algorithm (QAOA) as minimum

eigensolver routine.



```python

from docplex.mp.model import Model



from qiskit_optimization.algorithms import MinimumEigenOptimizer

from qiskit_optimization.translators import from_docplex_mp



from qiskit.primitives import Sampler



from qiskit_algorithms.utils import algorithm_globals

from qiskit_algorithms import QAOA

from qiskit_algorithms.optimizers import SPSA



# Generate a graph of 4 nodes

n = 4

edges = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (1, 2, 1.0), (2, 3, 1.0)]  # (node_i, node_j, weight)



# Formulate the problem as a Docplex model

model = Model()



# Create n binary variables

x = model.binary_var_list(n)



# Define the objective function to be maximized

model.maximize(model.sum(w * x[i] * (1 - x[j]) + w * (1 - x[i]) * x[j] for i, j, w in edges))



# Fix node 0 to be 1 to break the symmetry of the max-cut solution

model.add(x[0] == 1)



# Convert the Docplex model into a `QuadraticProgram` object

problem = from_docplex_mp(model)



# Run quantum algorithm QAOA on qasm simulator

seed = 1234

algorithm_globals.random_seed = seed



spsa = SPSA(maxiter=250)

sampler = Sampler()

qaoa = QAOA(sampler=sampler, optimizer=spsa, reps=5)

algorithm = MinimumEigenOptimizer(qaoa)

result = algorithm.solve(problem)

print(result.prettyprint())  # prints solution, x=[1, 0, 1, 0], the cost, fval=4

```



### Further examples



Learning path notebooks may be found in the

[optimization tutorials](https://qiskit-community.github.io/qiskit-optimization/tutorials/index.html) section

of the documentation and are a great place to start.



----------------------------------------------------------------------------------------------------



## Contribution Guidelines



If you'd like to contribute to Qiskit, please take a look at our

[contribution guidelines](https://github.com/qiskit-community/qiskit-optimization/blob/main/CONTRIBUTING.md).

This project adheres to Qiskit's [code of conduct](https://github.com/qiskit-community/qiskit-optimization/blob/main/CODE_OF_CONDUCT.md).

By participating, you are expected to uphold this code.



We use [GitHub issues](https://github.com/qiskit-community/qiskit-optimization/issues) for tracking requests and bugs. Please

[join the Qiskit Slack community](https://qisk.it/join-slack)

and for discussion and simple questions.

For questions that are more suited for a forum, we use the **Qiskit** tag in [Stack Overflow](https://stackoverflow.com/questions/tagged/qiskit).



## Authors and Citation



Optimization was inspired, authored and brought about by the collective work of a team of researchers.

Optimization continues to grow with the help and work of

[many people](https://github.com/qiskit-community/qiskit-optimization/graphs/contributors), who contribute

to the project at different levels.

If you use Qiskit, please cite as per the provided

[BibTeX file](https://github.com/Qiskit/qiskit/blob/main/CITATION.bib).



## License



This project uses the [Apache License 2.0](https://github.com/qiskit-community/qiskit-optimization/blob/main/LICENSE.txt).