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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 GateSX(mc.Power):
r"""Single qubit :math:`\sqrt{X}` gate.
**Matrix representation:**
.. math::
\sqrt{\operatorname{X}} = \frac{1}{2} \begin{pmatrix}
1+i & 1-i \\
1-i & 1+i\\
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateSX()
SX
>>> GateSX().matrix()
[0.5 + 0.5*I, 0.5 - 0.5*I]
[0.5 - 0.5*I, 0.5 + 0.5*I]
<BLANKLINE>
>>> c = Circuit().push(GateSX(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── SX @ q[0]
<BLANKLINE>
>>> GateSX().power(2), GateSX().inverse()
(X, SX†)
>>> GateSX().decompose()
1-qubit circuit with 4 instructions:
├── S† @ q[0]
├── H @ q[0]
├── S† @ q[0]
└── U(0, 0, 0, (1/4)*pi) @ q[0]
<BLANKLINE>
"""
_name = "SX"
name = "SX"
def __init__(self):
super().__init__(mc.GateX(), 1 / 2)
[docs]
def inverse(self):
return GateSXDG()
[docs]
def isopalias(self):
return True
def _control(self, n):
return control_one_defined(n, self, mc.GateCSX())
def _power(self, p):
# SX * SX = X
if p % 4 == 2:
return mc.GateX()
# (SX * SX) * (SX * SX) = X * X = ID
if p % 4 == 0:
return mc.GateID()
# (SX * SX * SX) * SX = ID => SX * SX * SX = SX†
if p % 4 == 3:
return mc.GateSXDG()
# SX * SX * SX * SX = ID => SX^(n*4) * SX = ID * SX = SX
if p % 4 == 1:
return self
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.GateSDG(), q)
circ.push(mc.GateH(), q)
circ.push(mc.GateSDG(), q)
circ.push(mc.GateU(0, 0, 0, pi / 4), q)
return circ
[docs]
class GateSXDG(mc.Inverse):
r"""Single qubit :math:`\sqrt{X}^\dagger` gate (conjugate transpose of the :math:`\sqrt{X}` gate).
**Matrix representation:**
.. math::
\sqrt{\operatorname{X}}^\dagger = \frac{1}{2} \begin{pmatrix}
1-i & 1+i \\
1+i & 1-i\\
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateSXDG()
SX†
>>> GateSXDG().matrix()
[0.5 - 0.5*I, 0.5 + 0.5*I]
[0.5 + 0.5*I, 0.5 - 0.5*I]
<BLANKLINE>
>>> c = Circuit().push(GateSXDG(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── SX† @ q[0]
<BLANKLINE>
>>> GateSXDG().power(2), GateSXDG().inverse()
(SX†**2, SX)
>>> GateSXDG().decompose()
1-qubit circuit with 4 instructions:
├── S @ q[0]
├── H @ q[0]
├── S @ q[0]
└── U(0, 0, 0, (-1/4)*pi) @ q[0]
<BLANKLINE>
"""
def __init__(self):
super().__init__(GateSX())
[docs]
def inverse(self):
return GateSX()
[docs]
def isopalias(self):
return True
def _control(self, n):
return control_one_defined(n, self, mc.GateCSXDG())
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateS(), q)
circ.push(mc.GateH(), q)
circ.push(mc.GateS(), q)
circ.push(mc.GateU(0, 0, 0, -pi / 4), q)
return circ
