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base.py
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base.py
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import polynomial
import lagrange_psr
import constant
import numpy as np
import qiskit
def zz_measure(qc: qiskit.QuantumCircuit):
_00 = np.asarray([1, 0, 0, 0])
_01 = np.asarray([0, 1, 0, 0])
_10 = np.asarray([0, 0, 1, 0])
_11 = np.asarray([0, 0, 0, 1])
psi = qiskit.quantum_info.Statevector(qc)
return np.abs(np.inner(_00, psi))**2 - np.abs(np.inner(_01, psi))**2 - np.abs(np.inner(_10, psi))**2 + np.abs(np.inner(_11, psi))**2
def measure(qc: qiskit.QuantumCircuit, qubits, cbits=[]):
"""Measuring the quantu circuit which fully measurement gates
Args:
- qc (QuantumCircuit): Measured circuit
- qubits (np.ndarray): List of measured qubit
Returns:
- float: Frequency of 00.. cbit
"""
n = len(qubits)
if cbits == []:
cbits = qubits.copy()
for i in range(0, n):
qc.measure(qubits[i], cbits[i])
counts = qiskit.execute(
qc, backend=constant.backend,
shots=constant.num_shots).result().get_counts()
return counts.get("0" * len(qubits), 0) / constant.num_shots
def upper_matrix(M):
"""Example:
[[1,2,3,4],
[5,6,7,8],
[9,10,12,13],
[14,15,16,17]]
Return:
[4, 7, 13]
Args:
M (np.ndarray): non-zero square matrix
Returns:
np.ndarray: zic-zac elements except the first
"""
upper_elements = []
for i in range(0, M.shape[0]):
for j in range(i + 1, M.shape[0], 2):
upper_elements.append(M[i, j])
return np.expand_dims(np.asarray(upper_elements[1:]), 1)
def calculate_Lambda(lambdas: list, x):
"""Convert the exponential expression to polynomial expression
Args:
lambdas (list): assume that we have already the eigenvalues = {\lambda_i}
x: parameter value of quantum gate
Returns:
polynomial.Polynomial: polynomial expression of quantum gate
"""
#
n = len(lambdas)
Ss = []
for k in range(0, n):
P = np.exp(-1j * x * lambdas[k])
Vs = []
for l in range(0, n):
if l != k:
P = P / (lambdas[k] - lambdas[l])
Vs.append(polynomial.Polymonial([-lambdas[l], 1]))
V = polynomial.multiXPoly(Vs)
Ss.append(V.multiX(P))
S = polynomial.addXPoly(Ss)
return S
def calculate_Lambda_matrix(lambdas: np.ndarray, x: float):
"""Return square matrix which contains Lambda_i * Lambda_j at each element
Args:
lambdas (np.ndarray): eigenvalues of quantum gate
x (float): phase
Returns:
np.ndarray: square matrix
"""
Lambdas = calculate_Lambda(lambdas, x).coeff
M = np.zeros([len(Lambdas), len(Lambdas)], dtype=np.complex128)
for i in range(0, len(Lambdas)):
for j in range(0, len(Lambdas)):
M[i, j] = np.conjugate(Lambdas[i]) * Lambdas[j]
return M
def calculate_Tau_matrix(B, G, n):
Tau = np.zeros([n, n], dtype=np.complex128)
for i in range(0, n):
for j in range(0, n):
Tau[i, j] = np.linalg.matrix_power(
G, i) @ B @ np.linalg.matrix_power(G, j)
return Tau
def check_symmetric(matrix, rtol=1e-05, atol=1e-08):
return np.allclose(matrix, np.conjugate(matrix.T), rtol=rtol, atol=atol)
def unit_vector(i, length):
unit_vector = np.zeros((length))
unit_vector[i] = 1.0
return unit_vector
def create_log_step_sizes(low, high, size):
steps = []
step = low
while (step < high):
steps.append(step)
step = step + size
size = size * 1.01
return steps
def create_logsin_step_sizes(low, high, size):
steps = []
step = low
while (step < high):
if step < 0.1:
steps.append(np.sin(step))
else:
steps.append((step))
step = step + size
size = size * 1.01
return np.round(steps, 2)
def second_derivative_2psr(f, thetas, i, j, alpha=np.pi/3):
length = thetas.shape[0]
k1 = f(thetas + alpha*(unit_vector(i, length) + unit_vector(j, length)))
k2 = -f(thetas + alpha * (unit_vector(i, length) - unit_vector(j, length)))
k3 = -f(thetas - alpha * (unit_vector(i, length) - unit_vector(j, length)))
k4 = f(thetas - alpha*(unit_vector(i, length) + unit_vector(j, length)))
return (1/(4*(np.sin(alpha))**2))*(k1 + k2 + k3 + k4)
def second_derivative_4psr(f, thetas, i, j):
alpha1 = np.pi/2
alpha2 = np.pi
d1 = 1j
d2 = 1j*(-1 + np.sqrt(2)) / 2
length = thetas.shape[0]
k1A = -1*(f(thetas + alpha1*unit_vector(i, length) + alpha1*unit_vector(j, length))
- f(thetas + alpha1*unit_vector(i, length) - alpha1*unit_vector(j, length)))
k1B = -(1-np.sqrt(2))/2*(f(thetas + alpha1*unit_vector(i, length) + alpha2*unit_vector(j, length))
- f(thetas + alpha1*unit_vector(i, length) - alpha2*unit_vector(j, length)))
k2A = 1*(f(thetas - alpha1*unit_vector(i, length) + alpha1*unit_vector(j, length))
- f(thetas - alpha1*unit_vector(i, length) - alpha1*unit_vector(j, length)))
k2B = (1-np.sqrt(2))/2*(f(thetas - alpha1*unit_vector(i, length) + alpha2*unit_vector(j, length))
- f(thetas - alpha1*unit_vector(i, length) - alpha2*unit_vector(j, length)))
k3A = -(1-np.sqrt(2))/2*(f(thetas + alpha2*unit_vector(i, length) + alpha1*unit_vector(j, length))
- f(thetas + alpha2*unit_vector(i, length) - alpha1*unit_vector(j, length)))
k3B = -(1-np.sqrt(2))**2/4*(f(thetas + alpha2*unit_vector(i, length) + alpha2*unit_vector(j, length))
+ f(thetas + alpha2*unit_vector(i, length) - alpha2*unit_vector(j, length)))
k4A = (1-np.sqrt(2))/2*(f(thetas - alpha2*unit_vector(i, length) + alpha1*unit_vector(j, length))
- f(thetas - alpha2*unit_vector(i, length) - alpha1*unit_vector(j, length)))
k4B = (1-np.sqrt(2))**2/4*(f(thetas - alpha2*unit_vector(i, length) + alpha2*unit_vector(j, length))
+ f(thetas - alpha2*unit_vector(i, length) - alpha2*unit_vector(j, length)))
return (-1j/2)**2*(k1A + k1B + k2A + k2B + k3A + k3B + k4A + k4B)
# def two_prx(f, thetas, j):
# length = thetas.shape[0]
# return constant.two_term_psr['r'] * (
# f(thetas + constant.two_term_psr['s'] * unit_vector(j, length)) -
# f(thetas - constant.two_term_psr['s'] * unit_vector(j, length))
# )
def two_prx_hLMG(f, thetas, h):
lambdas = constant.lambdas
length = thetas.shape[0]
alphas, d = lagrange_psr.lagrange_psr(lambdas)
grad = np.zeros(length, dtype = np.complex128)
for i in range(0, length):
for j in range(0, len(d)):
grad[i] += d[j] * (
f(thetas + alphas[j]* unit_vector(i, length), h) -
f(thetas - alphas[j]* unit_vector(i, length), h)
)
return np.real((-1j)*grad)
def pseudo_two_prx(f, thetas, j, step_size):
length = thetas.shape[0]
return (1/(2*np.sin(step_size))) * (
f(thetas + step_size * unit_vector(j, length)) -
f(thetas - step_size * unit_vector(j, length))
)
def a_pseudo_two_prx(f_left, f_right, step_size):
return (1/(2*np.sin(step_size))) * (
f_left - f_right
)
def a_two_finite_diff(f_left, f_right, step_size):
return (1/(2*(step_size))) * (
f_left - f_right
)
def four_prx(f, thetas, j):
length = thetas.shape[0]
return - (constant.four_term_psr['d_plus'] * (
f(thetas + constant.four_term_psr['alpha'] * unit_vector(j, length)) -
f(thetas - constant.four_term_psr['alpha'] * unit_vector(j, length))
- constant.four_term_psr['d_minus'] * (
f(thetas + constant.four_term_psr['beta'] * unit_vector(j, length)) -
f(thetas - constant.four_term_psr['beta'] * unit_vector(j, length))
)
))
def two_finite_diff(f, thetas, j, step_size):
length = thetas.shape[0]
return (1 / (2*step_size))*(
f(thetas + step_size * unit_vector(j, length)) -
f(thetas - step_size * unit_vector(j, length)))
def true_grad(thetas):
"""
df value in fig 2. paper
"""
derivate_x = -(np.cos(thetas[1]/2)**2)*np.sin(thetas[0])
derivate_y = (np.sin(thetas[0]/2)**2)*np.sin(thetas[1])
derivate_z = 0
return np.asarray([derivate_x, derivate_y, derivate_z])
def f_analytic(thetas):
"""
f value in fig 2. paper
"""
return 1/2*(1 + np.cos(thetas[0]) + (-1 + np.cos(thetas[0])*np.cos(thetas[2])))
def pseudo_four_prx(f, thetas, j):
length = thetas.shape[0]
return np.real(- 1j/2*(constant.four_term_psr['d_plus'] * (
f(thetas + constant.four_term_psr['alpha'] * unit_vector(j, length)) -
f(thetas - constant.four_term_psr['alpha'] * unit_vector(j, length))
- constant.four_term_psr['d_minus'] * (
f(thetas + constant.four_term_psr['beta'] * unit_vector(j, length)) -
f(thetas - constant.four_term_psr['beta'] * unit_vector(j, length))
)
)))