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import mimiqcircuits.operations.gates.gate as mcg
from mimiqcircuits.matrices import umatrix
from mimiqcircuits.operations.utils import control_one_defined
import mimiqcircuits as mc
from sympy import I, pi, sin, cos, acos, Abs, simplify, exp, Expr, log, Matrix
import numpy as np
import sympy as sp
import symengine as se
from scipy.linalg import expm, logm
[docs]
class GateU(mcg.Gate):
r"""Single qubit generic unitary phase gate.
**Matrix representation:**
.. math::
\operatorname{U}(\theta, \phi, \lambda, \gamma) =
\mathrm{e}^{i\gamma}
\begin{pmatrix}
\cos\left(\frac{\theta}{2}\right) & -\mathrm{e}^{i\lambda}\sin\left(\frac{\theta}{2}\right)\\
\mathrm{e}^{i\phi}\sin\left(\frac{\theta}{2}\right) & \mathrm{e}^{i(\phi+\lambda)}\cos\left (\frac{\theta}{2}\right)
\end{pmatrix}
Parameters:
theta (float): Euler angle 1 in radians.
phi (float): Euler angle 2 in radians.
lambda (float): Euler angle 3 in radians.
gamma (float, optional): Euler angle 4 in radians (default is 0).
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta, phi, lmbda, gamma = symbols('theta phi lambda gamma')
>>> GateU(theta, phi, lmbda, gamma)
U(theta, phi, lambda, gamma)
>>> GateU(theta, phi, lmbda, gamma).matrix()
[exp(I*gamma)*cos((1/2)*theta), -exp(I*(gamma + lambda))*sin((1/2)*theta)]
[exp(I*(gamma + phi))*sin((1/2)*theta), exp(I*(gamma + lambda + phi))*cos((1/2)*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateU(theta, phi, lmbda, gamma), 0)
>>> c
1-qubit circuit with 1 instructions:
└── U(theta, phi, lambda, gamma) @ q[0]
<BLANKLINE>
>>> GateU(theta, phi, lmbda, gamma).power(2), GateU(theta, phi, lmbda, gamma).inverse()
(U(theta, phi, lambda, gamma)**2, U(-theta, -lambda, -phi, -gamma))
>>> GateU(theta, phi, lmbda, gamma).decompose()
1-qubit circuit with 1 instructions:
└── U(theta, phi, lambda, gamma) @ q[0]
<BLANKLINE>
>>> c = Circuit().push(GateU(theta, phi, lmbda, gamma), 0)
>>> c
1-qubit circuit with 1 instructions:
└── U(theta, phi, lambda, gamma) @ q[0]
<BLANKLINE>
>>> GateU(theta, phi, lmbda, gamma).power(2), GateU(theta, phi, lmbda, gamma).inverse()
(U(theta, phi, lambda, gamma)**2, U(-theta, -lambda, -phi, -gamma))
>>> GateU(theta, phi, lmbda, gamma).decompose()
1-qubit circuit with 1 instructions:
└── U(theta, phi, lambda, gamma) @ q[0]
<BLANKLINE>
"""
_name = "U"
_num_qubits = 1
_qregsizes = [1]
_parnames = ("theta", "phi", "lmbda", "gamma")
def __init__(self, theta, phi, lmbda, gamma=0.0):
self.theta = theta
self.phi = phi
self.lmbda = lmbda
self.gamma = gamma
def _matrix(self):
return umatrix(self.theta, self.phi, self.lmbda, self.gamma)
[docs]
def inverse(self):
return GateU(-self.theta, -self.lmbda, -self.phi, -self.gamma)
def _control(self, n):
return control_one_defined(
n, self, mc.GateCU(self.theta, self.phi, self.lmbda, self.gamma)
)
def _power(self, p):
if self.is_symbolic():
return mc.Power(self, p)
def to_numeric(value):
if isinstance(value, (se.Basic,sp.Basic)) and value == se.pi or value == se.pi:
return float(value)
return value
theta_value = to_numeric(self.theta)
phi_value = to_numeric(self.phi)
lambda_value = to_numeric(self.lmbda)
gamma_value = to_numeric(self.gamma)
numeric_gate = GateU(theta_value, phi_value, lambda_value, gamma_value)
matrix = numeric_gate.matrix().tolist()
matrix_np = np.array(self.convert_to_numeric(matrix))
pow_matrix = expm(p * logm(matrix_np))
# Compute the angles based on the resulting matrix and prevent error raising becouse of division by zero.
with np.errstate(divide='ignore'):
theta_p = 2 * np.arccos(np.abs(pow_matrix[0, 0]))
gamma_p = np.angle(pow_matrix[0, 0])
phi_p = np.angle(pow_matrix[1, 0] / np.sin(theta_p / 2)) - gamma_p
lambda_p = np.angle(-pow_matrix[0, 1] / np.sin(theta_p / 2)) - gamma_p
return GateU(theta_p, phi_p, lambda_p, gamma_p)
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(self, q)
return circ
[docs]
def convert_to_numeric(self, matrix):
"""
Convert a symbolic matrix to a numeric numpy array.
"""
return np.array([[complex(elem.evalf()) for elem in row] for row in matrix], dtype=np.complex128)
