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Express an optimization problem

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To express a problem to be solved, create an instance of a Problem and set the problem_type to one of ProblemType.ising, ProblemType.pubo, or their grouped analogues, 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 described in the following section, 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, or as a list of Term objects (or, where supported, grouped term objects, for example: SlcTerm).

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)

Grouped term objects can be included in the terms list just like monomial terms.

terms = [
    Term(c=-9, indices=[0]),
    Term(c=-3, indices=[1,0]),
    Term(c=5, indices=[2,0]),
    SlcTerm(
        terms=[
            Term(c=1, indices=[0]),
            Term(c=-1, indices=[1]),
        ],
        c=2
    )
]
problem = Problem(name="My Other Problem", terms=terms, problem_type=ProblemType.ising_grouped)

Note

Only a subset of optimization solvers currently support grouped terms. Refer to the SlcTerm documentation for details.

Individually

You can supply each Term object 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])

You can also supply grouped term objects individually by calling the particular method on the Problem according to the particular grouped term type, or through an overloaded add_terms method.

Currently, squared linear combinations are the only enabled grouped terms and may be added via add_slc_term. For more information, see Problem.add_slc_term and SlcTerm.

problem = Problem(name="My Other Difficult Problem", problem_type=ProblemType.ising)
subterms = [
    Term(c=1, indices=[0]),
    Term(c=-2, indices=[1]),
    Term(c=1, indices=[2]),
    Term(c=-1, indices=[])
]
problem.add_slc_term(terms=subterms, c=2)

An alternate way to supply squared linear combination (slc) grouped terms is to supply them as a list of pairs where the first entry is the coefficient, and second is the variable id. Constants are supplied as (c, None).

problem.add_slc_term(
    terms=[(1,0), (-2,1), (1,2), (-1,None)],
    c=2
)

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)

Next steps

Now that you've created an optimization problem, learn how to solve it by applying a solver.