kaiwu.conversion package#

Module contents#

A collection of conversion utilities.

kaiwu.conversion.ising_matrix_to_qubo_matrix(ising_mat, remove_linear_bit=True)#

Convert an Ising matrix to a QUBO matrix.

Args:

ising_mat (np.ndarray): The Ising matrix.

remove_linear_bit (bool): When converting QUBO to Ising, an auxiliary variable is introduced for linear terms. Whether to remove the last spin variable. Default is True.

Returns:

tuple: A QUBO matrix and the corresponding bias term.

  • qubo_mat (np.ndarray): The QUBO matrix.

  • bias (float): The constant value representing the difference between the QUBO and Ising formulations.

Examples:
>>> import numpy as np
>>> import kaiwu as kw
>>> matrix = -np.array([[ 0. ,  1. ,  0. ,  1. ,  1. ],
...                     [ 1. ,  0. ,  0. ,  1.,   1. ],
...                     [ 0. ,  0. ,  0. ,  1.,   1. ],
...                     [ 1. ,  1.,   1. ,  0. ,  1. ],
...                     [ 1. ,  1.,   1. ,  1. ,  0. ]])
>>> _qubo_mat, _ = kw.conversion.ising_matrix_to_qubo_matrix(matrix)
>>> _qubo_mat
array([[-4.,  8.,  0.,  8.],
       [-0., -4.,  0.,  8.],
       [-0., -0., -0.,  8.],
       [-0., -0., -0., -8.]])
kaiwu.conversion.qubo_matrix_to_ising_matrix(qubo_mat)#

Convert a QUBO matrix to an Ising matrix.

Args:

qubo_mat (np.ndarray): The QUBO matrix.

Returns:
tuple: An Ising matrix and the corresponding bias term.

  • ising_mat (np.ndarray): The Ising matrix.

  • bias (float): The constant value representing the difference between the QUBO and Ising formulations.

Examples:
>>> import numpy as np
>>> import kaiwu as kw
>>> matrix = -np.array([[-4.,  8.,  0.,  8.],
...                     [-0., -4.,  0.,  8.],
...                     [-0., -0., -0.,  8.],
...                     [-0., -0., -0., -8.]])
>>> _ising_mat, _ = kw.conversion.qubo_matrix_to_ising_matrix(matrix)
>>> _ising_mat
array([[-0.,  1., -0.,  1.,  1.],
       [ 1., -0., -0.,  1.,  1.],
       [-0., -0., -0.,  1.,  1.],
       [ 1.,  1.,  1., -0.,  1.],
       [ 1.,  1.,  1.,  1., -0.]])
kaiwu.conversion.qubo_model_to_ising_model(qubo_model)#

Convert a QUBO model to a CIM Ising model.

Args:

qubo_model (QuboModel): The QUBO model.

Returns:

CimIsing: The resulting CIM Ising model.

Examples:
>>> import kaiwu as kw
>>> b1, b2 = kw.core.Binary("b1"), kw.core.Binary("b2")
>>> q = b1 + b2 + b1*b2
>>> q_model = kw.qubo.QuboModel(q)
>>> ci = kw.conversion.qubo_model_to_ising_model(q_model)
>>> print(str(ci))
CIM Ising Details:
  CIM Ising Matrix:
    [[-0.    -0.125 -0.375]
     [-0.125 -0.    -0.375]
     [-0.375 -0.375 -0.   ]]
  CIM Ising Bias: 1.25
  CIM Ising Variables: b1, b2, __spin__
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