amplify.BinaryIntQuadraticModel

class BinaryIntQuadraticModel

Is the quadratic model which represents the QUBO model with integer coefficients.

The class abstracts a “logical model” from multivariate polynomial, matrix, and constraints. The “logical model” is a formulation for inputting into the ising machines. This class generates a logical model by reducing the order of multivariate polynomial to quadratic and reallocating variable index.

The class converts to a logical model from the below objects.

• Multivariate polynomial

  • Includes polynomial with the order greater than three.

• Matrix

• Constraint

  • Includes multiple constraints

Note

For more details of the conversion source, see __init__() and its examples.

Through attributes of this class, you can get a raw input model, a converted logical model, and mapping from an input model to a logical model.

Note

The following operators are defined for the class.

• Addition: a + b (__add__(), __radd__(), __iadd__())

__init__(*args, **kwargs)

Returns the QUBO quadratic model initialized by input and constraints.

Overloads:

• __init__(poly, constraints)

• __init__(matrix, constant, constraints)

Parameters:

• poly (BinaryIntPoly) –

  • polynomial of the QUBO model.

• matrix (BinaryIntMatrix) –

  • the QUBO matrix of the QUBO model

• constant (int, optional) –

  • a constant term of the QUBO model

• constraints (BinaryIntConstraint, BinaryIntConstraints, optional) –

  • constraints of the QUBO model

Example

>>> from amplify import (gen_symbols,
... BinaryIntQuadraticModel)
>>> from amplify.constraint import equal_to
>>> q = gen_symbols(BinaryIntQuadraticModel, 3)
>>> model = BinaryIntQuadraticModel(q[0] + q[1] + q[2], equal_to(q[0], 1))
>>> model.input_poly
q_0 + q_1 + q_2

>>> from amplify import (BinaryIntMatrix,
... BinaryIntQuadraticModel)
>>> mat = BinaryIntMatrix(3)
>>> mat[0, 1] = 1
>>> mat[0, 2] = 2
>>> mat[1, 2] = 3
>>> model = BinaryIntQuadraticModel(mat, 4)
>>> model.input_matrix
([[0, 1, 2],
 [0, 0, 3],
 [0, 0, 0]], 4)

Methods

__init__(*args, **kwargs)	Returns the QUBO quadratic model initialized by input and constraints.
check_constraints(*args, **kwargs)	Overloaded function.

Attributes

input_constraints	Returns the constraints of the QUBO quadratic model.
input_matrix	Equivalent to logical_matrix.
input_poly	Returns the input BinaryIntPoly.
logical_mapping	Returns the mapping from input varieties to logical varieties.
logical_matrix	Returns the pair of BinaryIntMatrix and the constant term of the QUBO quadratic model.
logical_model_matrix	Is almost same as logical_matrix, but includes the constraint terms.
logical_model_poly	Is almost same as logical_poly, but includes the constraint terms.
logical_poly	Returns BinaryIntPoly, which represents the QUBO quadratic model.
num_input_vars	Returns the number of variables in the input QUBO quadratic model.
num_logical_vars	Returns the number of variables in the converted QUBO quadratic model.
substituion_multiplier

check_constraints(*args, **kwargs)

Overloaded function.

1. check_constraints(self: amplify.BinaryIntQuadraticModel, arg0: List[int]) -> List[Tuple[amplify.BinaryIntConstraintTermRef, bool]]

no docstring

2. check_constraints(self: amplify.BinaryIntQuadraticModel, arg0: Dict[int, int]) -> List[Tuple[amplify.BinaryIntConstraintTermRef, bool]]

3. check_constraints(self: amplify.BinaryIntQuadraticModel, arg0: function) -> List[Tuple[amplify.BinaryIntConstraintTermRef, bool]]

property input_constraints

Returns the constraints of the QUBO quadratic model.

Example

>>> from amplify import (gen_symbols,
... BinaryIntPoly,
... BinaryIntQuadraticModel)
>>> from amplify.constraint import equal_to
>>> q = gen_symbols(BinaryIntPoly, 1)
>>> model = BinaryIntQuadraticModel(equal_to(q[0], 1))
>>> eq = model.input_constraints.pop()
>>> eq.is_satisfied([0])
False
>>> eq.is_satisfied([1])
True

property input_matrix

Equivalent to logical_matrix.

property input_poly

Returns the input BinaryIntPoly.

Example

>>> from amplify import (BinaryIntPoly,
... BinaryIntQuadraticModel)
>>> poly = BinaryIntPoly({(0, 1, 2) : 1})
>>> model = BinaryIntQuadraticModel(poly)
>>> model.input_poly
q_0 q_1 q_2

property logical_mapping

Returns the mapping from input varieties to logical varieties.

Example

>>> from amplify import (BinaryIntMatrix,
... BinaryIntQuadraticModel)
>>> mat = BinaryIntMatrix(3)
>>> model = BinaryIntQuadraticModel(mat)
>>> model.logical_mapping
{2: 2, 0: 0, 1: 1}

property logical_matrix

Returns the pair of BinaryIntMatrix and the constant term of the QUBO quadratic model.

Example

>>> from amplify import (BinaryIntMatrix,
... BinaryIntQuadraticModel)
>>> mat = BinaryIntMatrix(3)
>>> mat[0, 1] = 1
>>> mat[0, 2] = 2
>>> mat[1, 2] = 3
>>> poly = mat.to_Poly()
>>> poly += 4
>>> model = BinaryIntQuadraticModel(poly)
>>> model.logical_matrix
([[0, 1, 2],
 [0, 0, 3],
 [0, 0, 0]], 4)

property logical_model_matrix

Is almost same as logical_matrix, but includes the constraint terms.

Example

>>> from amplify import (BinaryIntMatrix,
... BinaryIntQuadraticModel)
>>> from amplify.constraint import equal_to
>>> mat = BinaryIntMatrix(3)
>>> mat[0, 1] = 1
>>> mat[0, 2] = 2
>>> mat[1, 2] = 3
>>> poly = mat.to_Poly()
>>> poly += 4
>>> model = BinaryIntQuadraticModel(poly, equal_to(q[0], 1))
>>> model.logical_model_matrix
([[-1, 1, 2],
 [0, 0, 3],
 [0, 0, 0]], 5)

property logical_model_poly

Is almost same as logical_poly, but includes the constraint terms.

Example

>>> from amplify import (gen_symbols,
... BinaryIntQuadraticModel)
>>> from amplify.constraint import equal_to
>>> q = gen_symbols(BinaryIntQuadraticModel, 3)
>>> model = BinaryIntQuadraticModel(q[0] + q[1] + q[2], equal_to(q[0], 1))
>>> model.logical_model_poly
q_0 + q_1 + 1

property logical_poly

Returns BinaryIntPoly, which represents the QUBO quadratic model.

Note

The logical_poly variables don’t always correspond to the input_poly variables, even if input_poly is quadratic.

Example

>>> from amplify import (BinaryIntPoly,
... BinaryIntQuadraticModel)
>>> poly = BinaryIntPoly({(0, 1, 2) : 1})
>>> model = BinaryIntQuadraticModel(poly)
>>> model.logical_poly
q_0 q_1 + q_0 q_2 - q_0 q_3 + q_1 q_2 - q_1 q_3 - q_2 q_3 + q_3

property num_input_vars

Returns the number of variables in the input QUBO quadratic model.

Example

>>> from amplify import (BinaryIntPoly,
... BinaryIntQuadraticModel)
>>> poly = BinaryIntPoly({(0, 1, 2) : 1})
>>> model = BinaryIntQuadraticModel(poly)
>>> model.num_input_vars
3

property num_logical_vars

Returns the number of variables in the converted QUBO quadratic model.

Example

>>> from amplify import (BinaryIntPoly,
... BinaryIntQuadraticModel)
>>> poly = BinaryIntPoly({(0, 1, 2) : 1})
>>> model = BinaryIntQuadraticModel(poly)
>>> model.num_logical_vars
4