Problem Class

It may be useful to have a class that represents a problem. It includes the variables, constraints and objective function. This class can be used for constructing the quantum-compliant cost function.

Problem declarations

The class provides a method for declaring the problem:

• create_problem(var: Variables, constraint: Constraints, objective_functions: ObjectiveFunction)This method is used to declare the problem.

  • variables instances of the Variables class

  • constraints instances of the Constraints class

  • objective_functions instances of the ObjectiveFunction class.

and a method for obtaining the HUBO or PUBO formulation of the problem as qubovert PUBO object:

• write_the_final_cost_function( lambda_strategy: str, lambda_value: float = 1)This method is used to obtain the HUBO or PUBO formulation of the problem as qubovert PUBO object. The method takes two arguments:

  • lambda_strategy The strategy to be used for the conversion of the problem to HUBO or PUBO. The possible values are:

    • upper_bound_only_positive

    • maximum_coefficient

    • VLM

    • MOC

    • MOMC

    • upper lower bound naive

    • upper lower bound posiform and negaform method

    • manual

  • lambda_value The value of the lambda parameter if the use want to manually select it. The default value is 1.0.

Example:

from mqt.qao.constraints import Constraints
from mqt.qao.variables import Variables
from mqt.qao.objectivefunction import ObjectiveFunction

variables = Variables()
constraint = Constraints()
a0 = variables.add_binary_variable("a")
b0 = variables.add_discrete_variable("b", [-1, 1, 3])
c0 = variables.add_continuous_variable("c", -2, 2, 0.25, "", "")
constraint.add_constraint("c >= 1", True, True, False)
objective_function = ObjectiveFunction()
objective_function.add_objective_function(a0 + b0 * c0 + c0**2)
problem = Problem()
problem.create_problem(variables, constraint, objective_function)
pubo = problem.write_the_final_cost_function(lambda_strategy)