def single_gate_construct(mat, n, which_qubit):
r"""构建单量子比特门
Args:
mat (Variable): 输入的矩阵
n (int): 量子比特数
which_qubit (int): 输入矩阵所在的量子比特号
Returns:
Variable: 得到的单量子比特门矩阵
"""
idty = identity_generator(n - 1)
if which_qubit == 1:
mat = pp_kron(mat, idty)
elif which_qubit == n:
mat = pp_kron(idty, mat)
else:
I_top = identity_generator(which_qubit - 1)
I_bot = identity_generator(n - which_qubit)
mat = pp_kron(pp_kron(I_top, mat), I_bot)
return mat
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 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
def single_gate_construct(mat, n, which_qubit):
"""
:param mat: the input matrix
:param n: number of qubits
:param which_qubit: indicate which qubit the matrix is placed on
:return: the kronecker product of the matrix and identity
"""
idty = identity_generator(n - 1)
if which_qubit == 1:
mat = pp_kron(mat, idty)
elif which_qubit == n:
mat = pp_kron(idty, mat)
else:
I_top = identity_generator(which_qubit - 1)
I_bot = identity_generator(n - which_qubit)
mat = pp_kron(pp_kron(I_top, mat), I_bot)
return mat
def local_H_prob(cir, hamiltonian, shots=1024):
r"""
构造出Pauli测量电路并测量ancilla，处理实验结果来得到 ``H`` (只有一项)期望值的实验测量值。
Note:
这是内部函数，你并不需要直接调用到该函数。
"""
# Add one ancilla, which we later measure and process the result
new_cir = UAnsatz(cir.n + 1)
input_state = pp_kron(cir.run_state_vector(store_state=False),
init_state_gen(1))
# Used in fixed Rz gate
_theta = fluid.dygraph.to_variable(np.array([-np.pi / 2]))
op_list = hamiltonian.split(',')
# Set up pauli measurement circuit
for op in op_list:
element = op[0]
index = int(op[1:])
if element == 'x':
new_cir.h(index)
new_cir.cnot([index, cir.n])
elif element == 'z':
new_cir.cnot([index, cir.n])
elif element == 'y':
new_cir.rz(_theta, index)
new_cir.h(index)
new_cir.cnot([index, cir.n])
new_cir.run_state_vector(input_state)
prob_result = new_cir.measure(shots=shots, which_qubits=[cir.n])
if shots > 0:
if len(prob_result) == 1:
if '0' in prob_result:
result = (prob_result['0']) / shots
else:
result = (prob_result['1']) / shots
else:
result = (prob_result['0'] - prob_result['1']) / shots
else:
result = (prob_result['0'] - prob_result['1'])
return result