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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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# See the License for the specific language governing permissions and
# limitations under the License.
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import mimiqcircuits as mc
from mimiqcircuits.matrices import cis
from symengine import I, Matrix, cos, sin, pi
[docs]
class GateRXX(mc.Gate):
r"""Two qubit RXX gate (rotation about XX).
This gate is symmetric, and is maximally entangling at :math:`(\theta = \frac{\pi}{2})`
**Matrix representation:**
.. math::
\operatorname{RXX}(\theta) =\begin{pmatrix}
\cos(\frac{\theta}{2}) & 0 & 0 & -i\sin(\frac{\theta}{2}) \\
0 & \cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) & 0 \\
0 & -i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) & 0 \\
-i\sin(\frac{\theta}{2}) & 0 & 0 & \cos(\frac{\theta}{2})
\end{pmatrix}
Parameters:
theta: The angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRXX(theta)
RXX(theta)
>>> c = Circuit()
>>> c.push(GateRXX(theta), 0, 1)
2-qubit circuit with 1 instructions:
└── RXX(theta) @ q[0,1]
<BLANKLINE>
>>> GateRXX(theta).power(2), GateRXX(theta).inverse()
(RXX(theta)**2, RXX(-theta))
>>> GateRXX(theta).matrix()
[cos((1/2)*theta), 0, 0, -I*sin((1/2)*theta)]
[0, cos((1/2)*theta), -I*sin((1/2)*theta), 0]
[0, -I*sin((1/2)*theta), cos((1/2)*theta), 0]
[-I*sin((1/2)*theta), 0, 0, cos((1/2)*theta)]
<BLANKLINE>
>>> GateRXX(theta).decompose()
2-qubit circuit with 7 instructions:
├── H @ q[0]
├── H @ q[1]
├── CX @ q[0], q[1]
├── RZ(theta) @ q[1]
├── CX @ q[0], q[1]
├── H @ q[1]
└── H @ q[0]
<BLANKLINE>
"""
_name = 'RXX'
_num_qubits = 2
_qregsizes = [2]
_parnames = ('theta',)
def __init__(self, theta):
self.theta = theta
def _matrix(self):
theta = self.theta
cos2 = cos(theta / 2)
sin2 = sin(theta / 2)
return (Matrix([[cos2, 0, 0, -I * sin2],
[0, cos2, -I * sin2, 0],
[0, -I * sin2, cos2, 0],
[-I * sin2, 0, 0, cos2]]))
[docs]
def inverse(self):
return GateRXX(-self.theta)
def _decompose(self, circ, qubits, bits):
a, b = range(self.num_qubits)
circ.push(mc.GateH(), a)
circ.push(mc.GateH(), b)
circ.push(mc.GateCX(), a, b)
circ.push(mc.GateRZ(self.theta), b)
circ.push(mc.GateCX(), a, b)
circ.push(mc.GateH(), b)
circ.push(mc.GateH(), a)
return circ
[docs]
class GateRYY(mc.Gate):
r"""Two qubit RYY gate (rotation about YY).
This gate is symmetric, and is maximally entangling at :math:`(\theta = \frac{\pi}{2})`
**Matrix representation:**
.. math::
\operatorname{RYY}(\theta) =\begin{pmatrix}
\cos(\frac{\theta}{2}) & 0 & 0 & i\sin(\frac{\theta}{2}) \\
0 & \cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) & 0 \\
0 & -i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) & 0 \\
i\sin(\frac{\theta}{2}) & 0 & 0 & \cos(\frac{\theta}{2})
\end{pmatrix}
Parameters:
theta (float): The angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRYY(theta)
RYY(theta)
>>> GateRYY(theta).matrix()
[cos((1/2)*theta), 0, 0, I*sin((1/2)*theta)]
[0, cos((1/2)*theta), -I*sin((1/2)*theta), 0]
[0, -I*sin((1/2)*theta), cos((1/2)*theta), 0]
[I*sin((1/2)*theta), 0, 0, cos((1/2)*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateRYY(theta), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── RYY(theta) @ q[0,1]
<BLANKLINE>
>>> GateRYY(theta).power(2), GateRYY(theta).inverse()
(RYY(theta)**2, RYY(-theta))
>>> GateRYY(theta).decompose()
2-qubit circuit with 7 instructions:
├── RX((1/2)*pi) @ q[0]
├── RX((1/2)*pi) @ q[1]
├── CX @ q[0], q[1]
├── RZ(theta) @ q[1]
├── CX @ q[0], q[1]
├── RX((-1/2)*pi) @ q[0]
└── RX((-1/2)*pi) @ q[1]
<BLANKLINE>
"""
_name = 'RYY'
_num_qubits = 2
_qregsizes = [2]
_parnames = ('theta',)
def __init__(self, theta):
self.theta = theta
def _matrix(self):
theta = self.theta
cos2 = cos(theta / 2)
sin2 = sin(theta / 2)
return Matrix([[cos2, 0, 0, I * sin2],
[0, cos2, -I * sin2, 0],
[0, -I * sin2, cos2, 0],
[I * sin2, 0, 0, cos2]])
[docs]
def inverse(self):
return GateRYY(-self.theta)
def _decompose(self, circ, qubits, bits):
a, b = range(self.num_qubits)
circ.push(mc.GateRX(pi/2), a)
circ.push(mc.GateRX(pi/2), b)
circ.push(mc.GateCX(), a, b)
circ.push(mc.GateRZ(self.theta), b)
circ.push(mc.GateCX(), a, b)
circ.push(mc.GateRX(-pi/2), a)
circ.push(mc.GateRX(-pi/2), b)
return circ
[docs]
class GateRZZ(mc.Gate):
r"""Two qubit RZZ gate (rotation about ZZ)..
This gate is symmetric, and is maximally entangling at :math:`(\theta = \frac{\pi}{2})`
**Matrix representation:**
.. math::
\operatorname{RZZ}(\theta) = \begin{pmatrix}
e^{-i\frac{\theta}{2}} & 0 & 0 & 0 \\
0 & e^{i\frac{\theta}{2}} & 0 & 0 \\
0 & 0 & e^{i\frac{\theta}{2}} & 0 \\
0 & 0 & 0 & e^{-i\frac{\theta}{2}}
\end{pmatrix}
Parameters:
theta (float): The angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRZZ(theta)
RZZ(theta)
>>> GateRZZ(theta).matrix()
[exp(-1/2*I*theta), 0, 0, 0]
[0, exp(1/2*I*theta), 0, 0]
[0, 0, exp(1/2*I*theta), 0]
[0, 0, 0, exp(-1/2*I*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateRZZ(theta), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── RZZ(theta) @ q[0,1]
<BLANKLINE>
>>> GateRZZ(theta).power(2), GateRZZ(theta).inverse()
(RZZ(theta)**2, RZZ(-theta))
>>> GateRZZ(theta).decompose()
2-qubit circuit with 3 instructions:
├── CX @ q[0], q[1]
├── RZ(theta) @ q[1]
└── CX @ q[0], q[1]
<BLANKLINE>
"""
_num_qubits = 2
_name = 'RZZ'
_parnames = ('theta',)
_qregsizes = [2]
def __init__(self, theta):
self.theta = theta
def _matrix(self):
return Matrix([[cis(-self.theta / 2), 0, 0, 0],
[0, cis(self.theta / 2), 0, 0],
[0, 0, cis(self.theta / 2), 0],
[0, 0, 0, cis(-self.theta / 2)]])
[docs]
def inverse(self):
return GateRZZ(-self.theta)
def _decompose(self, circ, qubits, bits):
a, b = qubits
circ.push(mc.GateCX(), a, b)
circ.push(mc.GateRZ(self.theta), b)
circ.push(mc.GateCX(), a, b)
return circ
[docs]
class GateRZX(mc.Gate):
r"""Two qubit RZX gate.
This gate is maximally entangling at :math:`(\theta = \frac{\pi}{2})`
**Matrix representation:**
.. math::
\operatorname{RZX}(\theta) =\begin{pmatrix}
\cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) & 0 & 0 \\
-i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) & 0 & 0 \\
0 & 0 & \cos(\frac{\theta}{2}) & i\sin(\frac{\theta}{2}) \\
0 & 0 & i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2})
\end{pmatrix}
Parameters:
theta (float): The angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRZX(theta)
RZX(theta)
>>> GateRZX(theta).matrix()
[cos((1/2)*theta), -I*sin((1/2)*theta), 0, 0]
[-I*sin((1/2)*theta), cos((1/2)*theta), 0, 0]
[0, 0, cos((1/2)*theta), I*sin((1/2)*theta)]
[0, 0, I*sin((1/2)*theta), cos((1/2)*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateRZX(theta), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── RZX(theta) @ q[0,1]
<BLANKLINE>
>>> GateRZX(theta).power(2), GateRZX(theta).inverse()
(RZX(theta)**2, RZX(-theta))
>>> GateRZX(theta).decompose()
2-qubit circuit with 5 instructions:
├── H @ q[1]
├── CX @ q[0], q[1]
├── RZ(theta) @ q[1]
├── CX @ q[0], q[1]
└── H @ q[1]
<BLANKLINE>
"""
_num_qubits = 2
_name = 'RZX'
_parnames = ('theta',)
_qregsizes = [2]
def __init__(self, theta):
self.theta = theta
def _matrix(self):
theta = self.theta
cos2 = cos(theta / 2)
sin2 = sin(theta / 2)
return Matrix([
[cos2, -I * sin2, 0, 0],
[-I * sin2, cos2, 0, 0],
[0, 0, cos2, I * sin2],
[0, 0, I * sin2, cos2]
])
[docs]
def inverse(self):
return GateRZX(-self.theta)
def _decompose(self, circ, qubits, bits):
a, b = range(self.num_qubits)
circ.push(mc.GateH(), b)
circ.push(mc.GateCX(), a, b)
circ.push(mc.GateRZ(self.theta), b)
circ.push(mc.GateCX(), a, b)
circ.push(mc.GateH(), b)
return circ
[docs]
class GateXXplusYY(mc.Gate):
r"""Two qubit parametric XXplusYY gate.
Also known as an XY gate. Its action is to induce a coherent rotation by some angle between :math:`\ket{10}` and :math:`\ket{01}`.
**Matrix representation:**
.. math::
\operatorname{(XX+YY)}(\theta, \beta)= \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & \cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2})e^{i\beta} & 0\\
0 & -i\sin(\frac{\theta}{2})e^{-i\beta} & \cos(\frac{\theta}{2}) & 0\\
0 & 0 & 0 & 1
\end{pmatrix}
Parameters:
theta: The angle in radians.
beta: The phase angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta, beta = symbols('theta beta')
>>> GateXXplusYY(theta, beta)
XXplusYY(theta, beta)
>>> GateXXplusYY(theta, beta).matrix()
[1.0, 0, 0, 0]
[0, cos((1/2)*theta), (sin(beta) - I*cos(beta))*sin((1/2)*theta), 0]
[0, I*(I*sin(beta) - cos(beta))*sin((1/2)*theta), cos((1/2)*theta), 0]
[0, 0, 0, 1.0]
<BLANKLINE>
>>> c = Circuit().push(GateXXplusYY(theta, beta), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── XXplusYY(theta, beta) @ q[0,1]
<BLANKLINE>
>>> GateXXplusYY(theta, beta).power(2), GateXXplusYY(theta, beta).inverse()
(XXplusYY(theta, beta)**2, XXplusYY(-theta, beta))
>>> GateXXplusYY(theta, beta).decompose()
2-qubit circuit with 14 instructions:
├── RZ(beta) @ q[0]
├── RZ((-1/2)*pi) @ q[1]
├── SX @ q[1]
├── RZ((1/2)*pi) @ q[1]
├── S @ q[0]
├── CX @ q[1], q[0]
├── RY((-1/2)*theta) @ q[1]
├── RY((-1/2)*theta) @ q[0]
├── CX @ q[1], q[0]
├── S† @ q[0]
├── RZ((-1/2)*pi) @ q[1]
├── SX† @ q[1]
├── RZ((1/2)*pi) @ q[1]
└── RZ(-beta) @ q[0]
<BLANKLINE>
"""
_num_qubits = 2
_name = 'XXplusYY'
_parnames = ('theta', 'beta')
_qregsizes = [2]
def __init__(self, theta, beta):
self.theta = theta
self.beta = beta
def _matrix(self):
theta = self.theta
beta = self.beta
cos2 = cos(theta / 2)
sin2 = sin(theta / 2)
return Matrix([
[1, 0, 0, 0],
[0, cos2, -I * sin2 * cis(beta), 0],
[0, -I * sin2 * cis(-beta), cos2, 0],
[0, 0, 0, 1]
])
[docs]
def inverse(self):
return GateXXplusYY(-self.theta, self.beta)
def _decompose(self, circ, qubits, bits):
a, b = range(self.num_qubits)
circ.push(mc.GateRZ(self.beta), a)
circ.push(mc.GateRZ(-pi/2), b)
circ.push(mc.GateSX(), b)
circ.push(mc.GateRZ(pi/2), b)
circ.push(mc.GateS(), a)
circ.push(mc.GateCX(), b, a)
circ.push(mc.GateRY(-self.theta/2), b)
circ.push(mc.GateRY(-self.theta/2), a)
circ.push(mc.GateCX(), b, a)
circ.push(mc.GateSDG(), a)
circ.push(mc.GateRZ(-pi/2), b)
circ.push(mc.GateSXDG(), b)
circ.push(mc.GateRZ(pi/2), b)
circ.push(mc.GateRZ(-self.beta), a)
return circ
[docs]
class GateXXminusYY(mc.Gate):
r"""Two qubit parametric GateXXminusYY gate.
Its action is to induce a coherent rotation by some angle between :math:`\ket{00}` and :math:`\ket{11}`
**Matrix representation:**
.. math::
\operatorname{(XX-YY)}(\theta, \beta)=\begin{pmatrix}
\cos(\frac{\theta}{2}) & 0 & 0 & -i\sin(\frac{\theta}{2})e^{-i\beta} \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
-i\sin(\frac{\theta}{2})e^{i\beta} & 0 & 0 & \cos(\frac{\theta}{2})
\end{pmatrix}
Parameters:
theta (float): The angle in radians.
beta (float): The angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta, beta = symbols('theta beta')
>>> GateXXminusYY(theta, beta)
XXminusYY(theta, beta)
>>> GateXXminusYY(theta, beta).matrix()
[cos((1/2)*theta), 0, 0, I*(I*sin(beta) - cos(beta))*sin((1/2)*theta)]
[0, 1.0, 0, 0]
[0, 0, 1.0, 0]
[(sin(beta) - I*cos(beta))*sin((1/2)*theta), 0, 0, cos((1/2)*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateXXminusYY(theta, beta), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── XXminusYY(theta, beta) @ q[0,1]
<BLANKLINE>
>>> GateXXminusYY(theta, beta).power(2), GateXXminusYY(theta, beta).inverse()
(XXminusYY(theta, beta)**2, XXminusYY(-theta, beta))
>>> GateXXminusYY(theta, beta).decompose()
2-qubit circuit with 14 instructions:
├── RZ(-beta) @ q[1]
├── RZ((-1/2)*pi) @ q[0]
├── SX @ q[0]
├── RZ((1/2)*pi) @ q[0]
├── S @ q[1]
├── CX @ q[0], q[1]
├── RY((1/2)*theta) @ q[0]
├── RY((-1/2)*theta) @ q[1]
├── CX @ q[0], q[1]
├── S† @ q[1]
├── RZ((-1/2)*pi) @ q[0]
├── SX† @ q[0]
├── RZ((1/2)*pi) @ q[0]
└── RZ(beta) @ q[1]
<BLANKLINE>
"""
_num_qubits = 2
_name = 'XXminusYY'
_parnames = ('theta', 'beta')
_qregsizes = [2]
def __init__(self, theta, beta):
self.theta = theta
self.beta = beta
def _matrix(self):
theta = self.theta
beta = self.beta
cos2 = cos(theta / 2)
sin2 = sin(theta / 2)
return Matrix([
[cos2, 0, 0, -I * sin2 * cis(-beta)],
[0, 1, 0, 0],
[0, 0, 1, 0],
[-I * sin2 * cis(beta), 0, 0, cos2]
])
[docs]
def inverse(self):
return GateXXminusYY(-self.theta, self.beta)
def _decompose(self, circ, qubits, bits):
a, b = range(self.num_qubits)
circ.push(mc.GateRZ(-self.beta), b)
circ.push(mc.GateRZ(-pi/2), a)
circ.push(mc.GateSX(), a)
circ.push(mc.GateRZ(pi/2), a)
circ.push(mc.GateS(), b)
circ.push(mc.GateCX(), a, b)
circ.push(mc.GateRY(self.theta/2), a)
circ.push(mc.GateRY(-self.theta/2), b)
circ.push(mc.GateCX(), a, b)
circ.push(mc.GateSDG(), b)
circ.push(mc.GateRZ(-pi/2), a)
circ.push(mc.GateSXDG(), a)
circ.push(mc.GateRZ(pi/2), a)
circ.push(mc.GateRZ(self.beta), b)
return circ
