# -*- coding: utf-8 -*-
"""
模块: qubo
功能: QUBO矩阵和Ising矩阵相关转化
"""
from decimal import Decimal
import numpy as np
[文档]
def ising_matrix_to_qubo_matrix(ising_mat, remove_linear_bit=True, decimal=False):
"""Ising矩阵转QUBO矩阵
Args:
ising_mat (np.ndarray): Ising矩阵
remove_linear_bit (bool): QUBO转Ising时会增加一个辅助变量表示线性项。是否移除最后一个自旋变量。默认为True。
decimal (bool): 是否使用Decimal进行高精度计算，默认为False。
Returns:
tuple: QUBO矩阵和bias
- qubo_mat (np.ndarray): QUBO矩阵
- bias (float): QUBO与Ising相差的常数项
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.core.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.]])
"""
if decimal:
ising_mat = np.vectorize(str)(ising_mat)
ising_mat = np.vectorize(Decimal)(ising_mat)
ising_mat = (ising_mat + ising_mat.T) / 2
ising_mat_linear = None
if remove_linear_bit:
ising_mat_linear = ising_mat[-1, :-1] * 2
ising_mat = ising_mat[:-1, :-1]
qubo_mat = ising_mat * 4
diag_vec = -4 * np.sum(ising_mat, axis=0)
bias = np.sum(ising_mat)
if remove_linear_bit:
bias -= np.sum(ising_mat_linear)
diag_vec += 2 * ising_mat_linear
qubo_mat = np.triu(qubo_mat * 2)
np.fill_diagonal(qubo_mat, diag_vec)
qubo_mat = np.array(qubo_mat, dtype=np.float64)
return -qubo_mat, -float(bias)
[文档]
def qubo_matrix_to_ising_matrix(qubo_mat, decimal=False):
"""QUBO矩阵转Ising矩阵
Args:
qubo_mat (np.ndarray): QUBO矩阵
decimal (bool): 是否使用Decimal进行高精度计算，默认为False。
Returns:
tuple: Ising矩阵和bias
- ising_mat (np.ndarray): Ising矩阵
- bias (float): QUBO与Ising相差的常数项
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.core.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.]])
"""
if decimal:
qubo_mat = np.vectorize(str)(qubo_mat)
qubo_mat = np.vectorize(Decimal)(qubo_mat)
ising_size = qubo_mat.shape[0] + 1
ising_mat = np.zeros((ising_size, ising_size))
qubo_mat = (qubo_mat + qubo_mat.T) / 8
qubo_div_4_diagoal = np.diagonal(qubo_mat).copy()
qubo_div_4 = qubo_mat
np.fill_diagonal(qubo_div_4, 0)
ising_mat[:-1, :-1] = qubo_div_4
ising_mat[-1, :-1] = np.sum(qubo_div_4, axis=0) + qubo_div_4_diagoal
ising_mat[:-1, -1] = np.sum(qubo_div_4, axis=0) + qubo_div_4_diagoal
bias = np.sum(qubo_div_4) + np.sum(qubo_div_4_diagoal) * 2
ising_mat = np.array(ising_mat, dtype=np.float64)
return -ising_mat, float(bias)
if __name__ == "__main__":
import doctest
doctest.testmod()
