Problem parent class

Note that the problems or np modules will not be imported with from qubovert import *. You must import qubovert.problems explicitly. Thus this parent class is accessed with qubovert.problems.Problem.

class qubovert.problems.Problem(*args, **kwargs)

Problem.

This acts a parent class to all the QUBO and QUSO conversion problem classes. The __new__ method keeps track of the problem args. The repr method uses those input args, such that eval(repr(cls)) == cls. Finally, we define a __eq__ method to determine if two problems are the same. The rest of the methods are to be implemented in child classes.

Subclasses must define at least one of the following methods:: to_qubo, to_quso.

If at least one of them is defined, then they will both work. The same is true for to_pubo and to_puso. Problem inherits from Conversions, for more details see help(qubovert.utils.Conversions)

__new__.

Creates the object and keeps track of the input arguments and keyword arguments. Child classes should not change this. This method will be called before every __init__ is called. We use __new__ to keep track of input arguments instead of using __init__ so that child class implementations don’t have to worry about it. Ie child classes don’t have to call super().__init__(*args, **kwargs) in their __init__ method.

Parameters: arguments (Defined in child classes.) –
Returns: obj
Return type: instance of the child class.

convert_solution(solution, *args, **kwargs)

convert_solution.

Convert the solution to the QUBO to the solution to the problem. Should be implemented in child classes. If it is not implemented in the child class, then this function will by default return the same solution as what inputted.

Parameters

solution (iterable or dict.) – The QUBO or QUSO solution output. The QUBO solution output is either a list or tuple where indices specify the label of the variable and the element specifies whether it’s 0 or 1 for QUBO (or 1 or -1 for QUSO), or it can be a dictionary that maps the label of the variable to is value.
spin (bool.) – spin indicates whether solution is the solution to the boolean {0, 1} formulation of the problem or the spin {1, -1} formulation of the problem. This parameter usually does not matter, and it will be ignored if possible. The only time it is used is if solution contains all 1’s. In this case, it is unclear whether solution came from a spin or boolean formulation of the problem, and we will figure it out based on the spin parameter.

Returns

Return type

Implemented in the child class.

is_solution_valid(solution, *args, **kwargs)

is_solution_valid.

Returns whether or not the proposed solution is valid. Should be implemented in child classes. If it is not implemented in the child class, then this function will by default return True.

Parameters

solution (iterable or dict.) – solution can be the output of convert_solution, or the QUBO or QUSO solver output. The QUBO solution output is either a list or tuple where indices specify the label of the variable and the element specifies whether it’s 0 or 1 for QUBO (or 1 or -1 for QUSO), or it can be a dictionary that maps the label of the variable to is value.
spin (bool.) – spin indicates whether solution is the solution to the boolean {0, 1} formulation of the problem or the spin {1, -1} formulation of the problem. This parameter usually does not matter, and it will be ignored if possible. The only time it is used is if solution contains all 1’s. In this case, it is unclear whether solution came from a spin or boolean formulation of the problem, and we will figure it out based on the spin parameter.

Returns

valid – True if the proposed solution is valid, else False.

Return type

boolean.

property num_binary_variables

num_binary_variables.

The number of binary variables that the QUBO/QUSO uses. Should be implemented in the child class.

Returns: num – The number of variables in the QUBO/QUSO formulation.
Return type: int.

solve_bruteforce(*args, **kwargs)

solve_bruteforce.

Solve the problem bruteforce. THIS SHOULD NOT BE USED FOR LARGE PROBLEMS! This is implemented in the parent qubovert.utils.Problem class. Some problems use a lot of slack binary variables for their QUBO/QUSO formulations. If this is the case, then the child class for this problem should override this method with a better bruteforce solver. But, for problems that do not use slack variables, this method will suffice. It converts the problem to QUBO, solves it with qubovert.utils.solve_qubo_bruteforce, and then calls and returns convert_solution.

Parameters: aruments (arguments and keyword arguments.) – Contains args and kwargs for the to_qubo method. Also contains a all_solutions boolean flag, which indicates whether or not to return all the solutions, or just the best one found. all_solutions defaults to False.
Returns: res – If all_solutions is False, then res is just the output of the convert_solution method. If all_solutions is True, then res is a list of outputs of the convert_solution method, e.g. a converted solution for each solution that the bruteforce solver returns.
Return type: the output or outputs of the convert_solution method.

to_pubo(*args, **kwargs)

to_pubo.

Since the model is already degree two, self.to_pubo will simply return qubovert.utils.PUBOMatrix(self.to_qubo(*args, **kwargs)).

Returns: P – The upper triangular PUBO matrix, a PUBOMatrix object. For most practical purposes, you can use PUBOMatrix in the same way as an ordinary dictionary. For more information, see help(qubovert.utils.PUBOMatrix).
Return type: qubovert.utils.PUBOMatrix object.

to_puso(*args, **kwargs)

to_puso.

Create and return PUSO model representing the problem. Should be implemented in child classes. If this method is not implemented in the child class, then it simply calls to_pubo or to_quso and converts to a PUSO formulation.

Parameters

arguments (Defined in the child class.) – They should be parameters that define lagrange multipliers or factors in the QUSO model.

Returns

H – For most practical purposes, you can use PUSOMatrix in the same way as an ordinary dictionary. For more information, see help(qubovert.utils.PUSOMatrix).

Return type

qubovert.utils.PUSOMatrix object.

Raises

RecursionError` if neither to_pubo nor to_puso are define –
in the subclass. –

to_qubo(*args, **kwargs)

to_qubo.

Create and return upper triangular QUBO representing the problem. Should be implemented in child classes. If this method is not implemented in the child class, then it simply calls to_quso and converts the quso formulation to a QUBO formulation.

Parameters

arguments (Defined in the child class.) – They should be parameters that define lagrange multipliers or factors in the QUBO.

Returns

Q – The upper triangular QUBO matrix, a QUBOMatrix object. For most practical purposes, you can use QUBOMatrix in the same way as an ordinary dictionary. For more information, see help(qubovert.utils.QUBOMatrix).

Return type

qubovert.utils.QUBOMatrix object.

Raises

RecursionError` if neither to_qubo nor to_quso are define –
in the subclass. –

to_quso(*args, **kwargs)

to_quso.

Create and return QUSO model representing the problem. Should be implemented in child classes. If this method is not implemented in the child class, then it simply calls to_qubo and converts the QUBO formulation to an QUSO formulation.

Parameters

arguments (Defined in the child class.) – They should be parameters that define lagrange multipliers or factors in the QUSO model.

Returns

L – The upper triangular coupling matrix, where two element tuples represent couplings and one element tuples represent fields. For most practical purposes, you can use IsingCoupling in the same way as an ordinary dictionary. For more information, see help(qubovert.utils.QUSOMatrix).

Return type

qubovert.utils.QUSOMatrix object.

Raises

RecursionError` if neither to_qubo nor to_quso are define –
in the subclass. –