def partial_trace(rho_AB, dim1, dim2, A_or_B):
r"""计算量子态的偏迹。
Args:
rho_AB (ComplexVariable): 输入的量子态
dim1 (int): 系统A的维数
dim2 (int): 系统B的维数
A_or_B (int): 1或者2，1表示去除A，2表示去除B
Returns:
ComplexVariable: 量子态的偏迹
"""
if A_or_B == 2:
dim1, dim2 = dim2, dim1
idty_np = identity(dim2).astype("complex128")
idty_B = to_variable(idty_np)
zero_np = np_zeros([dim2, dim2], "complex128")
res = to_variable(zero_np)
for dim_j in range(dim1):
row_top = pp_zeros([1, dim_j], dtype="float64")
row_mid = ones([1, 1], dtype="float64")
row_bot = pp_zeros([1, dim1 - dim_j - 1], dtype="float64")
bra_j_re = concat([row_top, row_mid, row_bot], axis=1)
bra_j_im = pp_zeros([1, dim1], dtype="float64")
bra_j = ComplexVariable(bra_j_re, bra_j_im)
if A_or_B == 1:
row_tmp = pp_kron(bra_j, idty_B)
res = elementwise_add(
res,
matmul(
matmul(row_tmp, rho_AB),
pp_transpose(ComplexVariable(row_tmp.real, -row_tmp.imag),
perm=[1, 0]),
),
)
if A_or_B == 2:
row_tmp = pp_kron(idty_B, bra_j)
res = elementwise_add(
res,
matmul(
matmul(row_tmp, rho_AB),
pp_transpose(ComplexVariable(row_tmp.real, -row_tmp.imag),
perm=[1, 0]),
),
)
return res
def partial_trace(rho_AB, dim1, dim2, A_or_B):
r"""求AB复合系统下的偏迹
Args:
rho_AB (Variable): AB复合系统的密度矩阵
dim1 (int): A系统的维度
dim2 (int): B系统的维度
A_orB (int): 1表示求系统A，2表示求系统B
Returns：
ComplexVariable: 求得的偏迹
"""
# dim_total = dim1 * dim2
if A_or_B == 2:
dim1, dim2 = dim2, dim1
idty_np = identity(dim2).astype("complex64")
idty_B = to_variable(idty_np)
zero_np = np_zeros([dim2, dim2], "complex64")
res = to_variable(zero_np)
for dim_j in range(dim1):
row_top = pp_zeros([1, dim_j], dtype="float32")
row_mid = ones([1, 1], dtype="float32")
row_bot = pp_zeros([1, dim1 - dim_j - 1], dtype="float32")
bra_j_re = concat([row_top, row_mid, row_bot], axis=1)
bra_j_im = pp_zeros([1, dim1], dtype="float32")
bra_j = ComplexVariable(bra_j_re, bra_j_im)
if A_or_B == 1:
row_tmp = pp_kron(bra_j, idty_B)
res = elementwise_add(
res,
matmul(
matmul(row_tmp, rho_AB),
pp_transpose(ComplexVariable(row_tmp.real, -row_tmp.imag),
perm=[1, 0]),
),
)
if A_or_B == 2:
row_tmp = pp_kron(idty_B, bra_j)
res += matmul(
matmul(row_tmp, rho_AB),
pp_transpose(ComplexVariable(row_tmp.real, -row_tmp.imag),
perm=[1, 0]),
)
return res
def hermitian(matrix):
r"""计算矩阵的埃尔米特转置，即Hermitian transpose。
Args:
matrix (ComplexVariable): 需要埃尔米特转置的矩阵
Returns:
ComplexVariable: 输入矩阵的埃尔米特转置
代码示例:
.. code-block:: python
from paddle_quantum.utils import hermitian
from paddle import fluid
import numpy as np
with fluid.dygraph.guard():
rho = fluid.dygraph.to_variable(np.array([[1+1j, 2+2j], [3+3j, 4+4j]]))
print(hermitian(rho).numpy())
::
[[1.-1.j 3.-3.j]
[2.-2.j 4.-4.j]]
"""
matrix_dagger = pp_transpose(ComplexVariable(matrix.real, -matrix.imag),
perm=[1, 0])
return matrix_dagger
def partial_trace(rho_AB, dim1, dim2, A_or_B):
"""
:param rho_AB: the input density matrix
:param dim1: dimension for system A
:param dim2: dimension for system B
:param A_or_B: 1 or 2, choose the system that you want trace out.
:return: partial trace
"""
# dim_total = dim1 * dim2
if A_or_B == 2:
dim1, dim2 = dim2, dim1
idty_np = identity(dim2).astype("complex64")
idty_B = to_variable(idty_np)
zero_np = np_zeros([dim2, dim2], "complex64")
res = to_variable(zero_np)
for dim_j in range(dim1):
row_top = pp_zeros([1, dim_j], dtype="float32")
row_mid = ones([1, 1], dtype="float32")
row_bot = pp_zeros([1, dim1 - dim_j - 1], dtype="float32")
bra_j_re = concat([row_top, row_mid, row_bot], axis=1)
bra_j_im = pp_zeros([1, dim1], dtype="float32")
bra_j = ComplexVariable(bra_j_re, bra_j_im)
if A_or_B == 1:
row_tmp = pp_kron(bra_j, idty_B)
res = elementwise_add(
res,
matmul(
matmul(row_tmp, rho_AB),
pp_transpose(
ComplexVariable(row_tmp.real, -row_tmp.imag),
perm=[1, 0]), ), )
if A_or_B == 2:
row_tmp = pp_kron(idty_B, bra_j)
res += matmul(
matmul(row_tmp, rho_AB),
pp_transpose(
ComplexVariable(row_tmp.real, -row_tmp.imag), perm=[1, 0]),
)
return res