def __measure_parameterless(self, state, which_qubits, result_desired):
r"""进行 01 测量。
Args:
state (ComplexVariable): 输入的量子态
which_qubits (list): 测量作用的量子比特编号
result_desired (list): 期望得到的测量结果，如 ``"0"``、``"1"`` 或者 ``["0", "1"]``
Returns:
ComplexVariable: 测量坍塌后的量子态
ComplexVariable：测量坍塌得到的概率
list: 测量得到的结果（0 或 1）
"""
n = self.get_qubit_number()
assert len(which_qubits) == len(result_desired), \
"the length of qubits wanted to be measured and the result desired should be same"
op_list = [np.eye(2, dtype=np.complex128)] * n
for i, ele in zip(which_qubits, result_desired):
k = int(ele)
rho = np.zeros((2, 2), dtype=np.complex128)
rho[int(k), int(k)] = 1
op_list[i] = rho
if n > 1:
measure_operator = fluid.dygraph.to_variable(NKron(*op_list))
else:
measure_operator = fluid.dygraph.to_variable(op_list[0])
state_measured = matmul(matmul(measure_operator, state),
dagger(measure_operator))
prob = trace(
matmul(matmul(dagger(measure_operator), measure_operator),
state)).real
state_measured = elementwise_div(state_measured, prob)
return state_measured, prob, result_desired
def __measure_parameterless(self, state, which_qubits, result_desired):
r"""进行 01 测量。
Args:
state (Tensor): 输入的量子态
which_qubits (list): 测量作用的量子比特编号
result_desired (str): 期望得到的测量结果
Returns:
Tensor: 测量坍塌后的量子态
Tensor：测量坍塌得到的概率
str: 测量得到的结果
"""
n = self.get_qubit_number()
assert len(which_qubits) == len(result_desired), \
"the length of qubits wanted to be measured and the result desired should be same"
op_list = [np.eye(2, dtype=np.complex128)] * n
for i, ele in zip(which_qubits, result_desired):
k = int(ele)
rho = np.zeros((2, 2), dtype=np.complex128)
rho[int(k), int(k)] = 1
op_list[i] = rho
if n > 1:
measure_operator = paddle.to_tensor(NKron(*op_list))
else:
measure_operator = paddle.to_tensor(op_list[0])
state_measured = matmul(matmul(measure_operator, state),
dagger(measure_operator))
prob = real(
trace(
matmul(matmul(dagger(measure_operator), measure_operator),
state)))
state_measured = divide(state_measured, prob)
return state_measured, prob, result_desired
def __measure_parameterized(self, state, which_qubits, result_desired,
theta):
r"""进行参数化的测量。
Args:
state (Tensor): 输入的量子态
which_qubits (list): 测量作用的量子比特编号
result_desired (str): 期望得到的测量结果
theta (Tensor): 测量运算的参数
Returns:
Tensor: 测量坍塌后的量子态
Tensor：测量坍塌得到的概率
str: 测量得到的结果
"""
n = self.get_qubit_number()
assert len(which_qubits) == len(result_desired), \
"the length of qubits wanted to be measured and the result desired should be same"
op_list = [paddle.to_tensor(np.eye(2, dtype=np.complex128))] * n
for idx in range(0, len(which_qubits)):
i = which_qubits[idx]
ele = result_desired[idx]
if int(ele) == 0:
basis0 = paddle.to_tensor(
np.array([[1, 0], [0, 0]], dtype=np.complex128))
basis1 = paddle.to_tensor(
np.array([[0, 0], [0, 1]], dtype=np.complex128))
rho0 = multiply(basis0, cos(theta[idx]))
rho1 = multiply(basis1, sin(theta[idx]))
rho = add(rho0, rho1)
op_list[i] = rho
elif int(ele) == 1:
# rho = diag(concat([cos(theta[idx]), sin(theta[idx])]))
# rho = paddle.to_tensor(rho, zeros((2, 2), dtype="float64"))
basis0 = paddle.to_tensor(
np.array([[1, 0], [0, 0]], dtype=np.complex128))
basis1 = paddle.to_tensor(
np.array([[0, 0], [0, 1]], dtype=np.complex128))
rho0 = multiply(basis0, sin(theta[idx]))
rho1 = multiply(basis1, cos(theta[idx]))
rho = add(rho0, rho1)
op_list[i] = rho
else:
print("cannot recognize the result_desired.")
# rho = paddle.to_tensor(ones((2, 2), dtype="float64"), zeros((2, 2), dtype="float64"))
measure_operator = paddle.to_tensor(op_list[0])
if n > 1:
for idx in range(1, len(op_list)):
measure_operator = kron(measure_operator, op_list[idx])
state_measured = matmul(matmul(measure_operator, state),
dagger(measure_operator))
prob = real(
trace(
matmul(matmul(dagger(measure_operator), measure_operator),
state)))
state_measured = divide(state_measured, prob)
return state_measured, prob, result_desired
def __measure_parameterized(self, state, which_qubits, result_desired,
theta):
r"""进行参数化的测量。
Args:
state (ComplexVariable): 输入的量子态
which_qubits (list): 测量作用的量子比特编号
result_desired (list): 期望得到的测量结果，如 ``"0"``、``"1"`` 或者 ``["0", "1"]``
theta (Variable): 测量运算的参数
Returns:
ComplexVariable: 测量坍塌后的量子态
Variable：测量坍塌得到的概率
list: 测量得到的结果（0 或 1）
"""
n = self.get_qubit_number()
assert len(which_qubits) == len(result_desired), \
"the length of qubits wanted to be measured and the result desired should be same"
op_list = [fluid.dygraph.to_variable(np.eye(2, dtype=np.complex128))
] * n
for idx in range(0, len(which_qubits)):
i = which_qubits[idx]
ele = result_desired[idx]
if int(ele) == 0:
basis0 = fluid.dygraph.to_variable(
np.array([[1, 0], [0, 0]], dtype=np.complex128))
basis1 = fluid.dygraph.to_variable(
np.array([[0, 0], [0, 1]], dtype=np.complex128))
rho0 = elementwise_mul(basis0, cos(theta[idx]))
rho1 = elementwise_mul(basis1, sin(theta[idx]))
rho = elementwise_add(rho0, rho1)
op_list[i] = rho
elif int(ele) == 1:
# rho = diag(concat([cos(theta[idx]), sin(theta[idx])]))
# rho = ComplexVariable(rho, zeros((2, 2), dtype="float64"))
basis0 = fluid.dygraph.to_variable(
np.array([[1, 0], [0, 0]], dtype=np.complex128))
basis1 = fluid.dygraph.to_variable(
np.array([[0, 0], [0, 1]], dtype=np.complex128))
rho0 = elementwise_mul(basis0, sin(theta[idx]))
rho1 = elementwise_mul(basis1, cos(theta[idx]))
rho = elementwise_add(rho0, rho1)
op_list[i] = rho
else:
print("cannot recognize the results_desired.")
# rho = ComplexVariable(ones((2, 2), dtype="float64"), zeros((2, 2), dtype="float64"))
measure_operator = fluid.dygraph.to_variable(op_list[0])
if n > 1:
for idx in range(1, len(op_list)):
measure_operator = kron(measure_operator, op_list[idx])
state_measured = matmul(matmul(measure_operator, state),
dagger(measure_operator))
prob = trace(
matmul(matmul(dagger(measure_operator), measure_operator),
state)).real
state_measured = elementwise_div(state_measured, prob)
return state_measured, prob, result_desired
def forward(self):
# 生成初始的编码器 E 和解码器 D\n",
E = Encoder(self.theta)
E_dagger = dagger(E)
D = E_dagger
D_dagger = E
# 编码量子态 rho_in
rho_BA = matmul(matmul(E, self.rho_in), E_dagger)
# 取 partial_trace() 获得 rho_encode 与 rho_trash
rho_encode = partial_trace(rho_BA, 2**N_B, 2**N_A, 1)
rho_trash = partial_trace(rho_BA, 2**N_B, 2**N_A, 2)
# 解码得到量子态 rho_out
rho_CA = kron(self.rho_C, rho_encode)
rho_out = matmul(matmul(D, rho_CA), D_dagger)
# 通过 rho_trash 计算损失函数
zero_Hamiltonian = fluid.dygraph.to_variable(
np.diag([1, 0]).astype('complex128'))
loss = 1 - (trace(matmul(zero_Hamiltonian, rho_trash))).real
return loss, self.rho_in, rho_out
def forward(self, state_in, label):
"""
Args:
state_in: The input quantum state, shape [-1, 1, 2^n]
label: label for the input state, shape [-1, 1]
Returns:
The loss:
L = ((<Z> + 1)/2 + bias - label)^2
"""
# Numpy array -> variable
Ob = fluid.dygraph.to_variable(Observable(self.n))
label_pp = fluid.dygraph.to_variable(label)
Utheta = U_theta(self.theta, n=self.n, depth=self.depth)
U_dagger = dagger(Utheta)
state_out = matmul(matmul(state_in, Utheta), U_dagger)
E_Z = trace(matmul(state_out, Ob))
# map <Z> to the predict label
state_predict = E_Z.real * 0.5 + 0.5 + self.bias
loss = fluid.layers.reduce_mean((state_predict - label_pp)**2)
is_correct = fluid.layers.where(
fluid.layers.abs(state_predict - label_pp) < 0.5).shape[0]
acc = is_correct / label.shape[0]
return loss, acc, state_predict.numpy()
def forward(self, N):
# 施加量子神经网络
U = U_theta(self.theta, N)
# rho_tilde 是将 U 作用在 rho 后得到的量子态 U*rho*U^dagger
rho_tilde = matmul(matmul(U, self.rho), dagger(U))
# 计算损失函数
loss = trace(matmul(self.sigma, rho_tilde))
return loss.real, rho_tilde
def forward(self, N):
# Apply quantum neural network onto the initial state
U = U_theta(self.theta, N)
# rho_tilda is the quantum state obtained by acting U on rho, which is U*rho*U^dagger
rho_tilde = matmul(matmul(U, self.rho), dagger(U))
# Calculate loss function
loss = trace(matmul(self.sigma, rho_tilde))
return loss.real, rho_tilde
def run_density_matrix(self, input_state=None, store_state=True):
r"""运行当前的量子线路，输入输出的形式为密度矩阵。
Args:
input_state (ComplexVariable, optional): 输入的密度矩阵，默认为 :math:`|00...0\rangle \langle00...0|`
store_state (bool, optional): 是否存储输出的密度矩阵，默认为 ``True`` ，即存储
Returns:
ComplexVariable: 量子线路输出的密度矩阵
代码示例:
.. code-block:: python
import numpy as np
from paddle import fluid
from paddle_quantum.circuit import UAnsatz
n = 1
theta = np.ones(3)
input_state = np.diag(np.arange(2**n))+0j
input_state = input_state / np.trace(input_state)
with fluid.dygraph.guard():
input_state_var = fluid.dygraph.to_variable(input_state)
theta = fluid.dygraph.to_variable(theta)
cir = UAnsatz(n)
cir.rx(theta[0], 0)
cir.ry(theta[1], 0)
cir.rz(theta[2], 0)
density = cir.run_density_matrix(input_state_var).numpy()
print(f"密度矩阵是\n{density}")
::
密度矩阵是
[[ 0.35403671+0.j -0.47686058-0.03603751j]
[-0.47686058+0.03603751j 0.64596329+0.j ]]
"""
state = dygraph.to_variable(density_op(
self.n)) if input_state is None else input_state
assert state.real.shape == [2**self.n,
2**self.n], "The dimension is not right"
state = matmul(self.U, matmul(state, dagger(self.U)))
if store_state:
self.__state = state
# Add info about which function user called
self.__run_state = 'density_matrix'
return state
def run_density_matrix(self, input_state=None, store_state=True):
r"""运行当前的量子线路，输入输出的形式为密度矩阵。
Args:
input_state (Tensor, optional): 输入的密度矩阵，默认为 :math:`|00...0\rangle \langle00...0|`
store_state (bool, optional): 是否存储输出的密度矩阵，默认为 ``True`` ，即存储
Returns:
Tensor: 量子线路输出的密度矩阵
代码示例:
.. code-block:: python
import numpy as np
import paddle
from paddle_quantum.circuit import UAnsatz
from paddle_quantum.state import density_op
n = 1
theta = np.ones(3)
input_state = paddle.to_tensor(density_op(n))
theta = paddle.to_tensor(theta)
cir = UAnsatz(n)
cir.rx(theta[0], 0)
cir.ry(theta[1], 0)
cir.rz(theta[2], 0)
density_matrix = cir.run_density_matrix(input_state).numpy()
print(f"The output density matrix is\n{density_matrix}")
::
The output density matrix is
[[0.64596329+0.j 0.47686058+0.03603751j]
[0.47686058-0.03603751j 0.35403671+0.j ]]
"""
state = paddle.to_tensor(density_op(
self.n)) if input_state is None else input_state
assert paddle.real(state).shape == [2**self.n, 2**self.n
], "The dimension is not right"
state = matmul(self.U, matmul(state, dagger(self.U)))
if store_state:
self.__state = state
# Add info about which function user called
self.__run_state = 'density_matrix'
return state
def forward(self, H, N):
# 施加量子神经网络
U = U_theta(self.theta, N)
# 计算损失函数
loss_struct = matmul(matmul(dagger(U), H), U).real
# 输入计算基去计算每个子期望值，相当于取 U^dagger*H*U 的对角元
loss_components = [
loss_struct[0][0], loss_struct[1][1], loss_struct[2][2],
loss_struct[3][3]
]
# 最终加权求和后的损失函数
loss = 4 * loss_components[0] + 3 * loss_components[
1] + 2 * loss_components[2] + 1 * loss_components[3]
return loss, loss_components
def forward(self, H, N):
# Apply QNN onto the initial state
U = U_theta(self.theta, N)
# Calculate loss function
loss_struct = matmul(matmul(dagger(U), H), U).real
# Use computational basis to calculate each expectation value, which is the same
# as a diagonal element in U^dagger*H*U
loss_components = [
loss_struct[0][0], loss_struct[1][1], loss_struct[2][2],
loss_struct[3][3]
]
# Calculate the weighted loss function
loss = 4 * loss_components[0] + 3 * loss_components[
1] + 2 * loss_components[2] + 1 * loss_components[3]
return loss, loss_components
def forward(self, x):
rho_in = fluid.dygraph.to_variable(x)
E = Encoder(self.theta)
E_dagger = dagger(E)
D = E_dagger
D_dagger = E
rho_BA = matmul(matmul(E, rho_in), E_dagger)
rho_encode = partial_trace(rho_BA, 2**N_B, 2**N_A, 1)
rho_trash = partial_trace(rho_BA, 2**N_B, 2**N_A, 2)
rho_CA = kron(self.rho_C, rho_encode)
rho_out = matmul(matmul(D, rho_CA), D_dagger)
zero_Hamiltonian = fluid.dygraph.to_variable(
np.diag([1, 0]).astype('complex128'))
loss = 1 - (trace(matmul(zero_Hamiltonian, rho_trash))).real
return loss, rho_out, rho_encode