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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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from mimiqcircuits.operations.utils import control_one_defined
import mimiqcircuits as mc
from symengine import pi
[docs]
class GateSY(mc.Power):
r"""Single qubit :math:`\sqrt{Y}` gate.
See Also:
:class:`GateSYDG`, :class:`GateY`, :class:`Power`
**Matrix Representation**
.. math::
\operatorname{SY} =
\sqrt{\operatorname{Y}} =
\frac{1}{2}
\begin{pmatrix}
1+i & -1-i \\
1+i & 1+i
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateSY()
SY
>>> GateSY().matrix()
[0.5 + 0.5*I, -0.5 - 0.5*I]
[0.5 + 0.5*I, 0.5 + 0.5*I]
<BLANKLINE>
>>> c = Circuit()
>>> c.push(GateSY(), 1)
2-qubit circuit with 1 instructions:
└── SY @ q[1]
<BLANKLINE>
>>> c.push(GateSY(), 2)
3-qubit circuit with 2 instructions:
├── SY @ q[1]
└── SY @ q[2]
<BLANKLINE>
>>> power(GateSY(), 2)
Y**1.0
**Decomposition**
>>> GateSY().decompose()
1-qubit circuit with 4 instructions:
├── S @ q[0]
├── S @ q[0]
├── H @ q[0]
└── U(0, 0, 0, (1/4)*pi) @ q[0]
<BLANKLINE>
"""
_name = "SY"
def __init__(self):
super().__init__(mc.GateY(), 1 / 2)
[docs]
def inverse(self):
return GateSYDG()
[docs]
def isopalias(self):
return True
def _control(self, n):
return control_one_defined(n, self, mc.Control(1, GateSY()))
def _power(self, p):
return mc.Power(self, p)
def __str__(self):
return f"{self.name}"
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateS(), q)
circ.push(mc.GateS(), q)
circ.push(mc.GateH(), q)
circ.push(mc.GateU(0, 0, 0, pi / 4), q)
return circ
[docs]
class GateSYDG(mc.Inverse):
r"""Single qubit :math:`\sqrt{Y}^\dagger` gate (conjugate transpose of the :math:`\sqrt{Y}` gate).
See Also:
:class:`GateSY`, :class:`GateY`, :class:`Power`, :class:`Inverse`
**Matrix Representation**
.. math::
\operatorname{SYDG} =
\sqrt{\operatorname{Y}}^\dagger =
\frac{1}{2}
\begin{pmatrix}
1-i & 1-i \\
-1+i & 1-i
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateSYDG()
SY†
>>> GateSYDG().matrix()
[0.5 - 0.5*I, 0.5 - 0.5*I]
[-0.5 + 0.5*I, 0.5 - 0.5*I]
<BLANKLINE>
>>> c = Circuit()
>>> c.push(GateSYDG(), 1)
2-qubit circuit with 1 instructions:
└── SY† @ q[1]
<BLANKLINE>
>>> c.push(GateSYDG(), 2)
3-qubit circuit with 2 instructions:
├── SY† @ q[1]
└── SY† @ q[2]
<BLANKLINE>
>>> power(GateSYDG(), 2)
SY†**2
>>> inverse(GateSYDG())
SY
"""
def __init__(self):
super().__init__(GateSY())
[docs]
def inverse(self):
return GateSY()
[docs]
def isopalias(self):
return True
def _power(self, p):
return mc.Power(self, p)
def _control(self, n):
return control_one_defined(n, self, mc.Control(1, GateSYDG()))
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateU(0, 0, 0, -pi / 4), q)
circ.push(mc.GateH(), q)
circ.push(mc.GateSDG(), q)
circ.push(mc.GateSDG(), q)
return circ
