optimization-express-optimization-problem.md

author	description	ms.author	ms.date	ms.service	ms.subservice	ms.topic	title	uid
KittyYeungQ	This document provides a basic guide to express an optimization problem that could be later used with a solver in Azure Quantum.	kitty	02/01/2021	azure-quantum	optimization	how-to	Express an optimization problem	microsoft.quantum.optimization.express-problem

Express an optimization problem

To express a simple problem to be solved, create an instance of a Problem and set the problem_type to either ProblemType.ising or ProblemType.pubo. For more information, see ProblemType.

from azure.quantum.optimization import Problem, ProblemType, Term, ParallelTempering

problem = Problem(name="My First Problem", problem_type=ProblemType.ising)

Next, create an array of terms and add them to the problem:

terms = [
    Term(c=-9, indices=[0]),
    Term(c=-3, indices=[1,0]),
    Term(c=5, indices=[2,0]),
    Term(c=9, indices=[2,1]),
    Term(c=2, indices=[3,0]),
    Term(c=-4, indices=[3,1]),
    Term(c=4, indices=[3,2])
]

problem.add_terms(terms=terms)

Note

As descrbed below, there are multiple ways to supply terms to the problem.

Ways to supply problem terms

There are three ways to supply terms for a Problem: in the constructor, individually, and as a list of Term objects.

In the constructor

You can supply an array of Term objects in the constructor of a Problem.

terms = [
    Term(c=-9, indices=[0]),
    Term(c=-3, indices=[1,0]),
    Term(c=5, indices=[2,0])
]

problem = Problem(name="My Difficult Problem", terms=terms)

Individually

You can supply each term individually by calling the add_term method on the Problem.

problem = Problem(name="My Difficult Problem", problem_type=ProblemType.ising)
problem.add_term(c=-9, indices=[0])
problem.add_term(c=-3, indices=[1,0])
problem.add_term(c=5, indices=[2,0])

Add a list of terms

You can also supply a list of Term objects using the add-terms method on the Problem.

problem = Problem(name="My Difficult Problem")
terms = [
    Term(c=-9, indices=[0]),
    Term(c=-3, indices=[1,0]),
    Term(c=5, indices=[2,0]),
    Term(c=9, indices=[2,1]),
    Term(c=2, indices=[3,0]),
    Term(c=-4, indices=[3,1]),
    Term(c=4, indices=[3,2])
]

problem.add_terms(terms=terms)