def partial_trace(rho_AB, dim1, dim2, A_or_B):
r"""计算量子态的偏迹。
Args:
rho_AB (Tensor): 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表示计算系统A上的偏迹，2表示计算系统B上的偏迹
Returns:
Tensor: 输入的量子态的偏迹
"""
if A_or_B == 2:
dim1, dim2 = dim2, dim1
idty_np = np.identity(dim2).astype("complex128")
idty_B = to_tensor(idty_np)
zero_np = np.zeros([dim2, dim2], "complex128")
res = to_tensor(zero_np)
for dim_j in range(dim1):
row_top = zeros([1, dim_j], dtype="float64")
row_mid = ones([1, 1], dtype="float64")
row_bot = zeros([1, dim1 - dim_j - 1], dtype="float64")
bra_j = concat([row_top, row_mid, row_bot], axis=1)
bra_j = paddle.cast(bra_j, 'complex128')
if A_or_B == 1:
row_tmp = kron(bra_j, idty_B)
row_tmp_conj = paddle.conj(row_tmp)
res = add(
res,
matmul(
matmul(row_tmp, rho_AB),
transpose(row_tmp_conj, perm=[1, 0]),
),
)
if A_or_B == 2:
row_tmp = kron(idty_B, bra_j)
row_tmp_conj = paddle.conj(row_tmp)
res = add(
res,
matmul(
matmul(row_tmp, rho_AB),
transpose(row_tmp_conj, perm=[1, 0]),
),
)
return res
def dagger(matrix):
r"""计算矩阵的埃尔米特转置，即Hermitian transpose。
Args:
matrix (Tensor): 需要埃尔米特转置的矩阵
Returns:
Tensor: 输入矩阵的埃尔米特转置
代码示例:
.. code-block:: python
from paddle_quantum.utils import dagger
import numpy as np
rho = paddle.to_tensor(np.array([[1+1j, 2+2j], [3+3j, 4+4j]]))
print(dagger(rho).numpy())
::
[[1.-1.j 3.-3.j]
[2.-2.j 4.-4.j]]
"""
matrix_conj = paddle.conj(matrix)
matrix_dagger = transpose(matrix_conj, perm=[1, 0])
return matrix_dagger
def test_conj_api_real_number(self):
for dtype in self._dtypes:
input = rand([2, 20, 2, 3]).astype(dtype)
for place in self._places:
with dg.guard(place):
var_x = paddle.to_tensor(input)
result = paddle.conj(var_x).numpy()
target = np.conj(input)
self.assertTrue(np.array_equal(result, target))
def vec_expecval(H, vec):
r"""
It returns expectation value of H with respect to vector vec
Note:
这是内部函数，你并不需要直接调用到该函数。
"""
vec_conj = paddle.conj(vec)
result = paddle.sum(multiply(vec_conj, H_vec(H, vec)))
return result
def test_conj_static_mode(self):
def init_input_output(dtype):
input = rand([2, 20, 2, 3]).astype(dtype) + 1j * rand(
[2, 20, 2, 3]).astype(dtype)
return {'x': input}, np.conj(input)
for dtype in self._dtypes:
input_dict, np_res = init_input_output(dtype)
for place in self._places:
with static.program_guard(static.Program()):
x_dtype = np.complex64 if dtype == "float32" else np.complex128
x = static.data(
name="x", shape=[2, 20, 2, 3], dtype=x_dtype)
out = paddle.conj(x)
exe = static.Executor(place)
out_value = exe.run(feed=input_dict, fetch_list=[out.name])
self.assertTrue(np.array_equal(np_res, out_value[0]))
def run_state_vector(self, input_state=None, store_state=True):
r"""运行当前的量子线路，输入输出的形式为态矢量。
Args:
input_state (Tensor, optional): 输入的态矢量，默认为 :math:`|00...0\rangle`
store_state (Bool, optional): 是否存储输出的态矢量，默认为 ``True`` ，即存储
Returns:
Tensor: 量子线路输出的态矢量
代码示例:
.. code-block:: python
import numpy as np
import paddle
from paddle_quantum.circuit import UAnsatz
from paddle_quantum.state import vec
n = 2
theta = np.ones(3)
input_state = paddle.to_tensor(vec(n))
theta = paddle.to_tensor(theta)
cir = UAnsatz(n)
cir.h(0)
cir.ry(theta[0], 1)
cir.rz(theta[1], 1)
output_state = cir.run_state_vector(input_state).numpy()
print(f"The output state vector is {output_state}")
::
The output state vector is [[0.62054458+0.j 0.18316521+0.28526291j 0.62054458+0.j 0.18316521+0.28526291j]]
"""
state = init_state_gen(self.n,
0) if input_state is None else input_state
old_shape = state.shape
assert reduce(
lambda x, y: x * y, old_shape
) == 2**self.n, 'The length of the input vector is not right'
state = complex_reshape(state, (2**self.n, ))
state_conj = paddle.conj(state)
assert paddle.abs(paddle.real(paddle.sum(multiply(state_conj, state))) - 1) < 1e-8, \
'Input state is not a normalized vector'
for history_ele in self.__history:
if history_ele[0] == 'u':
state = StateTransfer(state, 'u', history_ele[1],
history_ele[2])
elif history_ele[0] in {'x', 'y', 'z', 'h'}:
state = StateTransfer(state,
history_ele[0],
history_ele[1],
params=history_ele[2])
elif history_ele[0] == 'SWAP':
state = StateTransfer(state, 'SWAP', history_ele[1])
elif history_ele[0] == 'CNOT':
state = StateTransfer(state, 'CNOT', history_ele[1])
if store_state:
self.__state = state
# Add info about which function user called
self.__run_state = 'state_vector'
return complex_reshape(state, old_shape)