def forward(self, input_state, H, N, N_SYS_B, D):
"""
Args:
input_state: The initial state with default |0..>
H: The target Hamiltonian
Returns:
The loss.
"""
out_state = U_theta(self.theta, input_state, N, D)
# rho_AB = utils.matmul(utils.matrix_conjugate_transpose(out_state), out_state)
rho_AB = matmul(
transpose(
fluid.framework.ComplexVariable(out_state.real,
-out_state.imag),
perm=[1, 0]),
out_state)
# compute the partial trace and three losses
rho_B = partial_trace(rho_AB, 2**(N - N_SYS_B), 2**(N_SYS_B), 1)
rho_B_squre = matmul(rho_B, rho_B)
loss1 = (trace(matmul(rho_B, H))).real
loss2 = (trace(rho_B_squre)).real * 2
loss3 = -(trace(matmul(rho_B_squre, rho_B))).real / 2
loss = loss1 + loss2 + loss3 # 损失函数
# option: if you want to check whether the imaginary part is 0, uncomment the following
# print('loss_iminary_part: ', loss.numpy()[1])
return loss - 3 / 2, rho_B
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 __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 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, H, N, N_SYS_B, beta, D):
# Apply quantum neural network onto the initial state
rho_AB = U_theta(self.initial_state, self.theta, N, D)
# Calculate the partial tarce to get the state rho_B of subsystem B
rho_B = partial_trace(rho_AB, 2**(N - N_SYS_B), 2**(N_SYS_B), 1)
# Calculate the three components of the loss function
rho_B_squre = matmul(rho_B, rho_B)
loss1 = (trace(matmul(rho_B, H))).real
loss2 = (trace(rho_B_squre)).real * 2 / beta
loss3 = -((trace(matmul(rho_B_squre, rho_B))).real + 3) / (2 * beta)
# Get the final loss function
loss = loss1 + loss2 + loss3
return loss, rho_B
def forward(self, H, N, N_SYS_B, beta, D):
# 施加量子神经网络
rho_AB = U_theta(self.initial_state, self.theta, N, D)
# 计算偏迹 partial trace 来获得子系统B所处的量子态 rho_B
rho_B = partial_trace(rho_AB, 2**(N - N_SYS_B), 2**(N_SYS_B), 1)
# 计算三个子损失函数
rho_B_squre = matmul(rho_B, rho_B)
loss1 = (trace(matmul(rho_B, H))).real
loss2 = (trace(rho_B_squre)).real * 2 / beta
loss3 = -((trace(matmul(rho_B_squre, rho_B))).real + 3) / (2 * beta)
# 最终的损失函数
loss = loss1 + loss2 + loss3
return loss, rho_B
def test_complex_x(self):
input = rand([2, 20, 2, 3]).astype(
self._dtype) + 1j * rand([2, 20, 2, 3]).astype(self._dtype)
for place in self._places:
with dg.guard(place):
var_x = dg.to_variable(input)
result = cpx.trace(var_x, offset=1, axis1=0, axis2=2).numpy()
target = np.trace(input, offset=1, axis1=0, axis2=2)
self.assertTrue(np.allclose(result, target))
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, 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), hermitian(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 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
def expecval(self, H):
r"""量子线路输出的量子态关于可观测量H的期望值。
Hint:
如果想输入的可观测量的矩阵为 :math:`0.7Z\otimes X\otimes I+0.2I\otimes Z\otimes I` 。则 ``H`` 应为 ``[[0.7, 'z0,x1'], [0.2, 'z1']]`` 。
Args:
H (list): 可观测量的相关信息
Returns:
Variable: 量子线路输出的量子态关于H的期望值
代码示例:
.. code-block:: python
import numpy as np
from paddle import fluid
from paddle_quantum.circuit import UAnsatz
n = 5
H_info = [[0.1, 'x1'], [0.2, 'y0,z4']]
theta = np.ones(3)
input_state = np.ones(2**n)+0j
input_state = input_state / np.linalg.norm(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.rz(theta[1], 1)
cir.rx(theta[2], 2)
cir.run_state_vector(input_state_var)
expect_value = cir.expecval(H_info).numpy()
print(f'计算得到的{H_info}期望值是{expect_value}')
::
计算得到的[[0.1, 'x1'], [0.2, 'y0,z4']]期望值是[0.05403023]
.. code-block:: python
import numpy as np
from paddle import fluid
from paddle_quantum.circuit import UAnsatz
n = 5
H_info = [[0.1, 'x1'], [0.2, 'y0,z4']]
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], 1)
cir.rz(theta[2], 2)
cir.run_density_matrix(input_state_var)
expect_value = cir.expecval(H_info).numpy()
print(f'计算得到的{H_info}期望值是{expect_value}')
::
计算得到的[[0.1, 'x1'], [0.2, 'y0,z4']]期望值是[-0.02171538]
"""
if self.__run_state == 'state_vector':
return vec_expecval(H, self.__state).real
elif self.__run_state == 'density_matrix':
state = self.__state
H_mat = fluid.dygraph.to_variable(pauli_str_to_matrix(H, self.n))
return trace(matmul(state, H_mat)).real
else:
# Raise error
raise ValueError(
"no state for measurement; please run the circuit first")