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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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import mimiqcircuits as mc
from mimiqcircuits.operations.utils import power_idempotent
from mimiqcircuits.operations.utils import control_one_defined
from symengine import pi, sqrt, Matrix, I
[docs]
class GateH(mc.Gate):
r"""Single qubit Hadamard gate.
**Matrix representation:**
.. math::
\operatorname{H} = \frac{1}{\sqrt{2}} \begin{pmatrix}
1 & 1 \\
1 & -1
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateH()
H
>>> GateH().matrix()
[0.707106781186548, 0.707106781186548]
[0.707106781186548, -0.707106781186548]
<BLANKLINE>
>>> c = Circuit().push(GateH(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── H @ q[0]
<BLANKLINE>
>>> GateH().power(2), GateH().inverse()
(ID, H)
>>> GateH().decompose()
1-qubit circuit with 1 instructions:
└── U((1/2)*pi, 0, pi, 0.0) @ q[0]
<BLANKLINE>
"""
_name = "H"
_num_qubits = 1
_qregsizes = [1]
[docs]
def inverse(self):
return self
def _power(self, p):
# H^(2n) = ID
# H^(2n+1) = H
return power_idempotent(self, p)
def _control(self, n):
return control_one_defined(n, self, mc.GateCH(), mc.Control(2, GateH()))
def _matrix(self):
return Matrix([[1, 1], [1, -1]]) / sqrt(2)
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateU(pi / 2, 0, pi), q)
return circ
[docs]
class GateHXY(mc.Gate):
r"""Single qubit HXY gate.
**Matrix representation:**
.. math::
\operatorname{HXY} = \frac{1}{\sqrt{2}} \begin{pmatrix}
0 & 1 - i \\
1 + i & 0
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateHXY()
HXY
>>> GateHXY().matrix()
[0, 0.707106781186548 - 0.707106781186548*I]
[0.707106781186548 + 0.707106781186548*I, 0]
<BLANKLINE>
>>> c = Circuit().push(GateHXY(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── HXY @ q[0]
<BLANKLINE>
>>> GateHXY().power(2), GateHXY().inverse()
(HXY**2, HXY)
>>> GateHXY().decompose()
1-qubit circuit with 5 instructions:
├── H @ q[0]
├── Z @ q[0]
├── H @ q[0]
├── S @ q[0]
└── U(0, 0, 0, (-1/4)*pi) @ q[0]
<BLANKLINE>
"""
_name = "HXY"
_num_qubits = 1
_qregsizes = [1]
[docs]
def inverse(self):
return self
def _power(self, p):
return mc.Power(GateHXY(), p)
def _control(self, n):
return control_one_defined(n, self, mc.Control(1, GateHXY()))
def _matrix(self):
return Matrix([[0, 1-I], [1+I, 0]]) / sqrt(2)
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateH(), q)
circ.push(mc.GateZ(), q)
circ.push(mc.GateH(), q)
circ.push(mc.GateS(), q)
circ.push(mc.GateU(0, 0, 0, -pi/4), q)
return circ
[docs]
class GateHYZ(mc.Gate):
r"""Single qubit HYZ gate.
**Matrix representation:**
.. math::
\operatorname{HYZ} = \frac{1}{\sqrt{2}} \begin{pmatrix}
1 & -i \\
i & -1
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateHYZ()
HYZ
>>> GateHYZ().matrix()
[0.707106781186548, -0.0 - 0.707106781186548*I]
[0.0 + 0.707106781186548*I, -0.707106781186548]
<BLANKLINE>
>>> c = Circuit().push(GateHYZ(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── HYZ @ q[0]
<BLANKLINE>
>>> GateHYZ().power(2), GateHYZ().inverse()
(HYZ**2, HYZ)
>>> GateHYZ().decompose()
1-qubit circuit with 5 instructions:
├── H @ q[0]
├── S @ q[0]
├── H @ q[0]
├── Z @ q[0]
└── U(0, 0, 0, (-1/4)*pi) @ q[0]
<BLANKLINE>
"""
_name = "HYZ"
_num_qubits = 1
_qregsizes = [1]
[docs]
def inverse(self):
return self
def _power(self, p):
return mc.Power(GateHYZ(), p)
def _control(self, n):
return control_one_defined(
n, self, mc.Control(1, GateHYZ()), mc.Control(2, GateHYZ())
)
def _matrix(self):
return Matrix([[1, -I], [I, -1]]) / sqrt(2)
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateH(), q)
circ.push(mc.GateS(), q)
circ.push(mc.GateH(), q)
circ.push(mc.GateZ(), q)
circ.push(mc.GateU(0, 0, 0, -pi/4), q)
return circ
[docs]
class GateHXZ(mc.Gate):
r"""Single qubit HXZ gate (alias for :class:`GateH`).
**Matrix representation:**
.. math::
\operatorname{H} = \frac{1}{\sqrt{2}} \begin{pmatrix}
1 & 1 \\
1 & -1
\end{pmatrix}
Examples:
The HXZ gate behaves exactly like the Hadamard gate:
>>> from mimiqcircuits import *
>>> GateHXZ()
H
>>> GateHXZ().matrix()
[0.707106781186548, 0.707106781186548]
[0.707106781186548, -0.707106781186548]
<BLANKLINE>
Adding GateHXZ to a circuit:
>>> c = Circuit().push(GateHXZ(), 0)
Power and inverse of the gate:
>>> GateHXZ().power(2), GateHXZ().inverse()
(ID, H)
Decomposition of the gate:
>>> GateHXZ().decompose()
1-qubit circuit with 1 instructions:
└── U((1/2)*pi, 0, pi, 0.0) @ q[0]
<BLANKLINE>
"""
def __new__(self):
return GateH()
