qiskit_addon_opt_mapper.converters.OptimizationProblemToQubo¶

class OptimizationProblemToQubo(penalty=None)[source]¶

Bases: OptimizationProblemConverter

Convert a given optimization problem in quadratic form into a QUBO problem.

Done by converting variables to binary and eliminating constraints. An optimization problem in quadratic form is a problem with quadratic objective function and linear constraints. A QUBO is a problem with quadratic objective function and no constraints. This combines several converters: IntegerToBinary, InequalityToPenalty, InequalityToEquality, EqualityToPenalty, and MaximizeToMinimize. The resulting HUBO problem can be directly mapped to an Ising Hamiltonian using the to_ising() function.

Examples

>>> from qiskit_addon_opt_mapper.problems import OptimizationProblem
>>> from qiskit_addon_opt_mapper.converters import OptimizationProblemToQubo
>>> problem = OptimizationProblem()
>>> # define a problem
>>> conv = OptimizationProblemToQubo()
>>> problem2 = conv.convert(problem)

Init method.

Parameters:: penalty (float | None) – Penalty factor to scale equality constraints that are added to objective. If None is passed, a penalty factor will be automatically calculated on every conversion.

__init__(penalty=None)[source]¶

Init method.

Parameters:: penalty (float | None) – Penalty factor to scale equality constraints that are added to objective. If None is passed, a penalty factor will be automatically calculated on every conversion.
Return type:: None

Methods

`__init__`([penalty])	Init method.
`convert`(problem)	Convert a optimization problem into a QUBO form.
`get_compatibility_msg`(problem)	Checks whether a given problem can be converted to a QUBO form.
`interpret`(x)	Convert the result of the converted problem back to that of the original problem.
`is_compatible`(problem)	Checks whether a given problem can be solved with the optimizer implementing this method.

Attributes

penalty

Returns the penalty factor used in conversion.

convert(problem)[source]¶

Convert a optimization problem into a QUBO form.

The new problem has no constraints and the objective function is quadratic.

Parameters:: problem (OptimizationProblem) – The problem with linear constraints to be solved.
Returns:: The problem converted in QUBO format as minimization problem.
Raises:: OptimizationError – In case of an incompatible problem.
Return type:: OptimizationProblem

static get_compatibility_msg(problem)[source]¶

Checks whether a given problem can be converted to a QUBO form.

If the problem is not compatible, this function returns a message explaining the incompatibility.

The following problems are not compatible: - Continuous variables are not supported. - Higher-order objective functions are not supported. - Quadratic constraints are not supported. - Higher-order constraints are not supported. - Constraints with float coefficients are not supported, because inequality constraints cannot be converted to equality constraints using integer slack variables.

Parameters:: problem (OptimizationProblem) – The optimization problem to check compatibility.
Returns:: A message describing the incompatibility.
Return type:: str

interpret(x)[source]¶

Convert the result of the converted problem back to that of the original problem.

Done by applying the interpret method of each converter in reverse order.

Parameters:: x (ndarray | list[float]) – The result of the converted problem.
Returns:: The result of the original problem.
Return type:: ndarray

is_compatible(problem)[source]¶

Checks whether a given problem can be solved with the optimizer implementing this method.

Parameters:: problem (OptimizationProblem) – The optimization problem to check compatibility.
Returns:: Returns True if the problem is compatible, False otherwise.
Return type:: bool

property penalty: float | None¶

Returns the penalty factor used in conversion.

Returns:: The penalty factor used in conversion.