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 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 trace 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 = paddle.real(trace(matmul(rho_B, H)))
loss2 = paddle.real(trace(rho_B_squre)) * 2 / beta
loss3 = -(paddle.real(trace(matmul(rho_B_squre, rho_B))) + 3) / (2 *
beta)
# Get the final loss function
loss = loss1 + loss2 + loss3
return loss, rho_B
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:
Tensor: 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
import paddle
from paddle_quantum.circuit import UAnsatz
n = 5
H_info = [[0.1, 'x1'], [0.2, 'y0,z4']]
theta = paddle.to_tensor(np.ones(3))
cir = UAnsatz(n)
cir.rx(theta[0], 0)
cir.rz(theta[1], 1)
cir.rx(theta[2], 2)
cir.run_state_vector()
expect_value = cir.expecval(H_info).numpy()
print(f'Calculated expectation value of {H_info} is {expect_value}')
::
Calculated expectation value of [[0.1, 'x1'], [0.2, 'y0,z4']] is [-0.1682942]
"""
if self.__run_state == 'state_vector':
return real(vec_expecval(H, self.__state))
elif self.__run_state == 'density_matrix':
state = self.__state
H_mat = paddle.to_tensor(pauli_str_to_matrix(H, self.n))
return real(trace(matmul(state, H_mat)))
else:
# Raise error
raise ValueError(
"no state for measurement; please run the circuit first")
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 paddle.real(loss), 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 (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):
# Apply QNN onto the initial state
U = U_theta(self.theta, N)
# Calculate loss function
loss_struct = paddle.real(matmul(matmul(dagger(U), H), U))
# 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 measure(self, which_qubits=None, shots=2**10, plot=False):
r"""对量子线路输出的量子态进行测量。
Warning:
当 ``plot`` 为 ``True`` 时，当前量子线路的量子比特数需要小于 6 ，否则无法绘制图片，会抛出异常。
Args:
which_qubits (list, optional): 要测量的qubit的编号，默认全都测量
shots (int, optional): 该量子线路输出的量子态的测量次数，默认为 1024 次；若为 0，则返回测量结果的精确概率分布
plot (bool, optional): 是否绘制测量结果图，默认为 ``False`` ，即不绘制
Returns:
dict: 测量的结果
代码示例:
.. code-block:: python
import paddle
from paddle_quantum.circuit import UAnsatz
cir = UAnsatz(2)
cir.h(0)
cir.cnot([0,1])
cir.run_state_vector()
result = cir.measure(shots = 2048, which_qubits = [1])
print(f"The results of measuring qubit 1 2048 times are {result}")
::
The results of measuring qubit 1 2048 times are {'0': 964, '1': 1084}
.. code-block:: python
import paddle
from paddle_quantum.circuit import UAnsatz
cir = UAnsatz(2)
cir.h(0)
cir.cnot([0,1])
cir.run_state_vector()
result = cir.measure(shots = 0, which_qubits = [1])
print(f"The probability distribution of measurement results on qubit 1 is {result}")
::
The probability distribution of measurement results on qubit 1 is {'0': 0.4999999999999999, '1': 0.4999999999999999}
"""
if self.__run_state == 'state_vector':
state = self.__state
elif self.__run_state == 'density_matrix':
# Take the diagonal of the density matrix as a probability distribution
diag = np.diag(self.__state.numpy())
state = paddle.to_tensor(np.sqrt(diag))
else:
# Raise error
raise ValueError(
"no state for measurement; please run the circuit first")
if shots == 0: # Returns probability distribution over all measurement results
dic2to10, dic10to2 = dic_between2and10(self.n)
result = {}
for i in range(2**self.n):
result[dic10to2[i]] = (real(state)[i]**2 +
imag(state)[i]**2).numpy()[0]
if which_qubits is not None:
new_result = [(self.__process_string(key, which_qubits), value)
for key, value in result.items()]
result = self.__process_similiar(new_result)
else:
if which_qubits is None: # Return all the qubits
result = measure_state(state, shots)
else:
assert all([e < self.n
for e in which_qubits]), 'Qubit index out of range'
which_qubits.sort() # Sort in ascending order
collapse_all = measure_state(state, shots)
new_collapse_all = [(self.__process_string(key, which_qubits),
value)
for key, value in collapse_all.items()]
result = self.__process_similiar(new_collapse_all)
return result if not plot else self.__measure_hist(
result, which_qubits, shots)
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)
