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# Copyright © 2022-2023 University of Strasbourg. All Rights Reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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# See the License for the specific language governing permissions and
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import mimiqcircuits.operations.gates.gate as mcg
from mimiqcircuits.operations.gates.standard.u import GateU
from mimiqcircuits.operations.gates.standard.deprecated import GateU3
from mimiqcircuits.operations.utils import control_one_defined
import mimiqcircuits as mc
from symengine import pi, Matrix, cos, sin, I, exp
[docs]
class GateRX(mcg.Gate):
r"""Single qubit Rotation gate around the axis :math:`\hat{x}`
**Matrix representation:**
.. math::
\operatorname{RX}(\theta) = \begin{pmatrix}
\cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\
-i\sin\frac{\theta}{2} & \cos\frac{\theta}{2}
\end{pmatrix}
Parameters:
theta: Rotation angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRX(theta)
RX(theta)
>>> GateRX(theta).matrix()
[cos((1/2)*theta), -I*sin((1/2)*theta)]
[-I*sin((1/2)*theta), cos((1/2)*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateRX(theta), 0)
>>> c
1-qubit circuit with 1 instructions:
└── RX(theta) @ q[0]
<BLANKLINE>
>>> GateRX(theta).power(2), GateRX(theta).inverse()
(RX(2*theta), RX(-theta))
>>> GateRX(theta).decompose()
1-qubit circuit with 1 instructions:
└── U(theta, (-1/2)*pi, (1/2)*pi, 0.0) @ q[0]
<BLANKLINE>
"""
_name = 'RX'
_num_qubits = 1
_qregsizes = [1]
_parnames = ('theta',)
def __init__(self, theta):
self.theta = theta
def _matrix(self):
return Matrix([
[cos(self.theta / 2), -I * sin(self.theta / 2)],
[-I * sin(self.theta / 2), cos(self.theta / 2)]
])
[docs]
def inverse(self):
return GateRX(-self.theta)
def _power(self, p):
return GateRX(self.theta * p)
def _control(self, n):
return control_one_defined(n, self, mc.GateCRX(self.theta))
def _decompose(self, circ, qubits, bits):
q = qubits[0]
circ.push(GateU(self.theta, -pi/2, pi/2), q)
return circ
[docs]
class GateRY(mcg.Gate):
r"""Single qubit Rotation gate around the axis :math:`\hat{y}`
**Matrix representation:**
.. math::
\operatorname{RY}(\theta) = \begin{pmatrix}
\cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\
\sin\frac{\theta}{2} & \cos\frac{\theta}{2}
\end{pmatrix}
Parameters:
theta (float): Rotation angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRY(theta)
RY(theta)
>>> GateRY(theta).matrix()
[cos((1/2)*theta), -sin((1/2)*theta)]
[sin((1/2)*theta), cos((1/2)*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateRY(theta), 0)
>>> c
1-qubit circuit with 1 instructions:
└── RY(theta) @ q[0]
<BLANKLINE>
>>> GateRY(theta).power(2), GateRY(theta).inverse()
(RY(2*theta), RY(-theta))
>>> GateRY(theta).decompose()
1-qubit circuit with 1 instructions:
└── U(theta, 0, 0, 0.0) @ q[0]
<BLANKLINE>
"""
_name = 'RY'
_num_qubits = 1
_qregsizes = [1]
_parnames = ('theta',)
def __init__(self, theta):
self.theta = theta
def _matrix(self):
return Matrix([
[cos(self.theta / 2), -sin(self.theta / 2)],
[sin(self.theta / 2), cos(self.theta / 2)]
])
[docs]
def inverse(self):
return GateRY(-self.theta)
def _power(self, p):
return GateRY(self.theta * p)
def _control(self, n):
control_one_defined(n, self, mc.GateCRY(self.theta))
def _decompose(self, circ, qubits, bits):
q = qubits[0]
circ.push(GateU(self.theta, 0, 0), q)
return circ
[docs]
class GateRZ(mcg.Gate):
r"""Single qubit Rotation gate around the axis :math:`\hat{z}`
**Matrix representation:**
.. math::
\operatorname{RZ}(\lambda) = \begin{pmatrix}
e^{-i\frac{\lambda}{2}} & 0 \\
0 & e^{i\frac{\lambda}{2}}
\end{pmatrix}
Parameters:
lambda: Rotation angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> lmbda = Symbol('lambda')
>>> GateRZ(lmbda)
RZ(lambda)
>>> GateRZ(lmbda).matrix()
[exp(-1/2*I*lambda), 0]
[0, exp(1/2*I*lambda)]
<BLANKLINE>
>>> c = Circuit().push(GateRZ(lmbda), 0)
>>> c
1-qubit circuit with 1 instructions:
└── RZ(lambda) @ q[0]
<BLANKLINE>
>>> GateRZ(lmbda).power(2), GateRZ(lmbda).inverse()
(RZ(2*lambda), RZ(-lambda))
>>> GateRZ(lmbda).decompose()
1-qubit circuit with 1 instructions:
└── U(0, 0, lambda, (-1/2)*lambda) @ q[0]
<BLANKLINE>
"""
_name = 'RZ'
_num_qubits = 1
_qregsizes = [1]
_parnames = ('lmbda',)
def __init__(self, lmbda):
self.lmbda = lmbda
def _matrix(self):
return Matrix([
[exp(-I * self.lmbda / 2), 0],
[0, exp(I * self.lmbda / 2)]
])
[docs]
def inverse(self):
return GateRZ(-self.lmbda)
def _power(self, p):
return GateRZ(self.lmbda * p)
def _control(self, n):
return control_one_defined(n, self, mc.GateCRZ(self.lmbda))
def _decompose(self, circ, qubits, bits):
q = qubits[0]
circ.push(GateU(0, 0, self.lmbda, -self.lmbda / 2), q)
return circ
[docs]
class GateR(mcg.Gate):
r"""Single qubit Rotation gate around the axis :math:`\cos(\phi)\hat{x} + \sin(\phi)\hat{y}`.
**Matrix representation:**
.. math::
\operatorname R(\theta,\phi) = \begin{pmatrix}
\cos \frac{\theta}{2} & -i e^{-i\phi} \sin \frac{\theta}{2} \\
-i e^{i \phi} \sin \frac{\theta}{2} & \cos \frac{\theta}{2}
\end{pmatrix}
Parameters:
theta (float): The rotation angle in radians.
phi (float): The axis of rotation in radians.
Example:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta, phi = symbols('theta phi')
>>> GateR(theta, phi)
R(theta, phi)
>>> GateR(theta, phi).matrix()
[cos((1/2)*theta), -I*exp(-I*phi)*sin((1/2)*theta)]
[-I*exp(I*phi)*sin((1/2)*theta), cos((1/2)*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateR(theta, phi), 0)
>>> GateR(theta, phi).power(2), GateR(theta, phi).inverse()
(R(2*theta, phi), R(-theta, phi))
>>> GateR(theta, phi).decompose()
1-qubit circuit with 1 instructions:
└── U3(theta, phi + (-1/2)*pi, -phi + (1/2)*pi) @ q[0]
<BLANKLINE>
"""
_name = 'R'
_num_qubits = 1
_qregsizes = [1]
_parnames = ('theta', 'phi')
def __init__(self, theta, phi):
self.theta = theta
self.phi = phi
def _matrix(self):
return Matrix([
[cos(self.theta / 2), -I * exp(-I * self.phi) * sin(self.theta / 2)],
[-I * exp(I * self.phi) * sin(self.theta / 2), cos(self.theta / 2)]
])
[docs]
def inverse(self):
return GateR(-self.theta, self.phi)
def _power(self, p):
return GateR(self.theta * p, self.phi)
def _decompose(self, circ, qubits, bits):
q = qubits[0]
circ.push(GateU3(self.theta, self.phi - pi/2, -self.phi + pi/2), q)
return circ
