kaiwu.sampler package

Module Contents

Module: sampler

Features: Provides a series of data post-processing tools

kaiwu.sampler.binarizer(c_list, var_type='spin', unique=True)

binarization.

Args:

c_list (np.ndarray): The data to be binarized obtained from the solver.

var_type (str): Variable type.

unique (bool): Deduplicate.

Returns:

np.ndarray: Binarized result.

Examples:

>>> import numpy as np
>>> import kaiwu as kw
>>> solutions = np.array([[-0.0032379, -0.00302381, -0.00080672, -0.00226754, 0.00400546],
...                      [-0.00063725, -0.00769352, 0.00140344, -0.00234206, -0.00034028],
...                      [0.0040677, -0.01139299, 0.00474858, 0.00274578, -0.00405366],
...                      [0.00765783, -0.00636498, 0.00964927, 0.00262433, -0.00175035],
...                      [0.01104296, -0.00444736, 0.01377671, 0.0061532, 0.00074683]])
>>> c_set = kw.sampler.binarizer(solutions)
>>> c_set
array([[-1, -1, -1, -1,  1],
       [-1, -1,  1, -1, -1],
       [ 1, -1,  1,  1, -1],
       [ 1, -1,  1,  1, -1],
       [ 1, -1,  1,  1,  1]])

kaiwu.sampler.binary_to_spin(c_set)

Binary to spin.

Args:

c_set (np.ndarray): Binary variable configuration.

Returns:

np.ndarray: Spin variable configuration.

Examples:

>>> import numpy as np
>>> import kaiwu as kw
>>> output = np.array([[0, 0, 0, 0],
...                    [0, 0, 0, 1],
...                    [0, 0, 1, 0],
...                    [0, 0, 1, 1],
...                    [0, 1, 0, 0],
...                    [0, 1, 0, 1],
...                    [0, 1, 1, 0],
...                    [0, 1, 1, 1],
...                    [1, 0, 0, 0],
...                    [1, 0, 0, 1],
...                    [1, 0, 1, 0],
...                    [1, 0, 1, 1],
...                    [1, 1, 0, 0],
...                    [1, 1, 0, 1],
...                    [1, 1, 1, 0],
...                    [1, 1, 1, 1]])
>>> kw.sampler.binary_to_spin(output)
array([[-1, -1, -1, -1],
       [-1, -1, -1,  1],
       [-1, -1,  1, -1],
       [-1, -1,  1,  1],
       [-1,  1, -1, -1],
       [-1,  1, -1,  1],
       [-1,  1,  1, -1],
       [-1,  1,  1,  1],
       [ 1, -1, -1, -1],
       [ 1, -1, -1,  1],
       [ 1, -1,  1, -1],
       [ 1, -1,  1,  1],
       [ 1,  1, -1, -1],
       [ 1,  1, -1,  1],
       [ 1,  1,  1, -1],
       [ 1,  1,  1,  1]])

kaiwu.sampler.calculate_qubo_value(qubo_matrix, offset, binary_configuration)

Q value calculator.

Args:

qubo_matrix (np.ndarray): QUBO matrix.

offset (float): Constant term.

binary_configuration (np.ndarray): Binary configuration

Returns:

output (float): Q value.

Examples:

>>> import numpy as np
>>> import kaiwu as kw
>>> matrix = np.array([[1., 0., 0.],
...                    [0., 1., 0.],
...                    [0., 0., 1.]])
>>> offset = 1.8
>>> binary_configuration = np.array([0, 1, 0])
>>> qubo_q = kw.sampler.calculate_qubo_value(matrix, offset, binary_configuration)
>>> print(qubo_q)
2.8

kaiwu.sampler.constraint_sampler(matrix, offset, var_index, c_set)

Constraint sampler

Args:

matrix (np.ndarray): QUBO matrix of constraints.

offset (float): Constant term.

var_index (list): Variables contained in the constraints, index table in all variables.

c_set (np.ndarray): Variable configuration.

Returns:

output (np.ndarray, np.ndarray): Variable configuration sorted by relaxation degree, relaxation degree.

Examples:

>>> import numpy as np
>>> import kaiwu as kw
>>> output = np.array([[0, 0, 0, 0],
...                    [0, 0, 0, 1],
...                    [0, 0, 1, 0],
...                    [0, 0, 1, 1],
...                    [0, 1, 0, 0],
...                    [0, 1, 0, 1],
...                    [0, 1, 1, 0],
...                    [0, 1, 1, 1],
...                    [1, 0, 0, 0],
...                    [1, 0, 0, 1],
...                    [1, 0, 1, 0],
...                    [1, 0, 1, 1],
...                    [1, 1, 0, 0],
...                    [1, 1, 0, 1],
...                    [1, 1, 1, 0],
...                    [1, 1, 1, 1]])
>>> matrix = np.array([[1., 0., 0.],
...                    [0., 1., 0.],
...                    [0., 0., 1.]])
>>> offset = -3
>>> var_index = [1, 2, 3]
>>> kw.sampler.constraint_sampler(matrix, offset, var_index, output)
(array([[0, 1, 1, 1],
       [1, 1, 1, 1],
       [0, 0, 1, 1],
       [0, 1, 0, 1],
       [0, 1, 1, 0],
       [1, 0, 1, 1],
       [1, 1, 0, 1],
       [1, 1, 1, 0],
       [0, 0, 0, 1],
       [0, 0, 1, 0],
       [0, 1, 0, 0],
       [1, 0, 0, 1],
       [1, 0, 1, 0],
       [1, 1, 0, 0],
       [0, 0, 0, 0],
       [1, 0, 0, 0]]), array([0., 0., 1., 1., 1., 1., 1., 1., 2., 2., 2., 2., 2., 2., 3., 3.]))

kaiwu.sampler.hamiltonian(matrix, c_list)

Hamiltonian calculation

Args:

matrix (np.ndarray): CPQC Ising matrix.

c_list (np.ndarray): The set of variable combinations to calculate the Hamiltonian.

Returns:

np.ndarray: Hamiltonian set.

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. ]])
>>> rng = np.random.default_rng(10)
>>> solver = kw.classical.SimulatedAnnealingOptimizer()
>>> output = solver.solve(matrix)
>>> h = kw.sampler.hamiltonian(matrix, output)
>>> h   
array([-0.60179257, -0.60179257, -0.60179257, -0.60179257, -0.60179257,
       -1.20358514, -0.60179257, -0.60179257, -0.60179257, -1.20358514])

kaiwu.sampler.negtail_flip(c_list)

Negative tail flip. Negtail flip is need for sampling CPQC Ising results generated by kaiwu.qubo. No negtail flip is needed for solving with direct input matrix.

Args:

c_list (np.ndarray): Variable combination set for negtail flip.

Returns:

None: in-place algorithm is used for this method. Modify input directly.

Examples:

>>> import numpy as np
>>> import kaiwu as kw
>>> mat = np.array([[ 1, -1, -1, -1,  1],
...                 [-1, -1,  1,  1, -1],
...                 [-1, -1,  1,  1,  1],
...                 [ 1,  1,  1,  1,  1],
...                 [-1,  1,  1, -1, -1],
...                 [ 1,  1,  1,  1, -1],
...                 [-1,  1,  1, -1,  1],
...                 [ 1, -1,  1,  1, -1],
...                 [-1, -1, -1,  1,  1]])
>>> kw.sampler.negtail_flip(mat)
>>> mat
array([[ 1, -1, -1, -1,  1],
       [ 1,  1, -1, -1,  1],
       [-1, -1,  1,  1,  1],
       [ 1,  1,  1,  1,  1],
       [ 1, -1, -1,  1,  1],
       [-1, -1, -1, -1,  1],
       [-1,  1,  1, -1,  1],
       [-1,  1, -1, -1,  1],
       [-1, -1, -1,  1,  1]])

kaiwu.sampler.optimal_sampler(matrix, c_set, bias=0.0, negtail_ff=False)

Optimal solution sampling.

Args:

matrix (np.ndarray): CPQC Ising matrix.

c_set (np.ndarray): Variable configuration.

bias (float): Constant term.

negtail_ff (bool): negtail_flip flag. The matrix of Ising model with quadratic linear terms requires negative tail flipping

Returns:

output (np.ndarray, np.ndarray): Variable configuration sorted by energy, energy.

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. ]])
>>> c_set = np.array([[ 1, -1,  1, -1, -1],
...                   [-1, -1,  1, -1, -1],
...                   [-1, -1, -1,  1,  1],
...                   [ 1,  1,  1, -1, -1],
...                   [ 1,  1,  1, -1, -1],
...                   [ 1,  1,  1, -1, -1]])
>>> kw.sampler.optimal_sampler(matrix, c_set, 0)
(array([[-1, -1, -1,  1,  1],
       [ 1,  1,  1, -1, -1],
       [ 1,  1,  1, -1, -1],
       [ 1,  1,  1, -1, -1],
       [ 1, -1,  1, -1, -1],
       [-1, -1,  1, -1, -1]]), array([-8., -8., -8., -8., -4.,  8.]))

kaiwu.sampler.random_sampler(matrix, negtail_ff=False)

Random sampler.

Args:

matrix (np.ndarray): CPQC Ising matrix.

negtail_ff (bool): negtail_flip flag. The matrix of Ising model with quadratic linear terms requires negative tail flipping

Returns:

np.ndarray: Binary configuration

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. ]])
>>> kw.sampler.random_sampler(matrix, False)  
array([[ 1,  1, -1, -1,  1]])

kaiwu.sampler.spin_to_binary(c_set)

Spin to binary

Args:

c_set (np.ndarray): Spin variable configuration.

Returns:

np.ndarray: Binary variable configuration.

Examples:

>>> import numpy as np
>>> import kaiwu as kw
>>> output = np.array([[-1, -1, -1, -1],
...                    [-1, -1, -1,  1],
...                    [-1, -1,  1, -1],
...                    [-1, -1,  1,  1],
...                    [-1,  1, -1, -1],
...                    [-1,  1, -1,  1],
...                    [-1,  1,  1, -1],
...                    [-1,  1,  1,  1],
...                    [ 1, -1, -1, -1],
...                    [ 1, -1, -1,  1],
...                    [ 1, -1,  1, -1],
...                    [ 1, -1,  1,  1],
...                    [ 1,  1, -1, -1],
...                    [ 1,  1, -1,  1],
...                    [ 1,  1,  1, -1],
...                    [ 1,  1,  1,  1]])
>>> kw.sampler.spin_to_binary(output)
array([[0., 0., 0., 0.],
       [0., 0., 0., 1.],
       [0., 0., 1., 0.],
       [0., 0., 1., 1.],
       [0., 1., 0., 0.],
       [0., 1., 0., 1.],
       [0., 1., 1., 0.],
       [0., 1., 1., 1.],
       [1., 0., 0., 0.],
       [1., 0., 0., 1.],
       [1., 0., 1., 0.],
       [1., 0., 1., 1.],
       [1., 1., 0., 0.],
       [1., 1., 0., 1.],
       [1., 1., 1., 0.],
       [1., 1., 1., 1.]])