Source code for mimiqcircuits.operations.gates.standard.s
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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.power import Power
from mimiqcircuits.operations.inverse import Inverse
from mimiqcircuits.operations.gates.standard.pauli import GateZ
from mimiqcircuits.operations.gates.standard.u import GateU
from mimiqcircuits.operations.utils import control_one_defined
import mimiqcircuits as mc
from symengine import pi
[docs]
class GateS(Power):
r"""Single qubit gate S.
It induces a :math:`\frac{\pi}{2}` phase gate.
**Matrix representation:**
.. math::
\operatorname{S} = \begin{pmatrix}
1 & 0 \\
0 & i
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateS()
S
>>> GateS().matrix()
[1.0, 0]
[0, 0.0 + 1.0*I]
<BLANKLINE>
>>> c = Circuit().push(GateS(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── S @ q[0]
<BLANKLINE>
>>> GateS().power(2), GateS().inverse()
(Z, S†)
>>> GateS().decompose()
1-qubit circuit with 1 instructions:
└── U(0, 0, (1/2)*pi, 0.0) @ q[0]
<BLANKLINE>
"""
_name = "S"
def __init__(self):
super().__init__(GateZ(), 1 / 2)
[docs]
def isopalias(self):
return True
[docs]
def inverse(self):
return GateSDG()
def _power(self, p):
pmod = p % 4
# sqrt(S) = T
if pmod == 1 / 2:
return mc.GateT()
# T * T^7 = S^2 * S^2 = Z * Z = ID => T^7 = TDG
if pmod == 7 / 2:
return mc.GateTDG()
# Z^(2n) = ID => S^(4n) = ID
if p % 4 == 0:
return mc.GateID()
# Z^(2n + 1) = Z => S^(4n + 1) = S
if p % 4 == 1:
return mc.GateS()
# S^(4n + 3) = SDG
if p % 4 == 3:
return mc.GateSDG()
# sqrt(Z) = S
if p % 2 == 0:
return mc.GateZ().power(p / 2)
def _control(self, n):
return control_one_defined(n, self, mc.GateCS())
def __str__(self):
return f"{self.name}"
def _decompose(self, circ, qubits, bits):
q = qubits[0]
circ.push(GateU(0, 0, pi / 2), q)
return circ
[docs]
class GateSDG(Inverse):
r"""Single qubit S-dagger gate (conjugate transpose of the S gate).
**Matrix representation:**
.. math::
\operatorname{S}^\dagger = \begin{pmatrix}
1 & 0 \\
0 & -i
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateSDG()
S†
>>> GateSDG().matrix()
[1.0, 0]
[0, 6.12323399573677e-17 - 1.0*I]
<BLANKLINE>
>>> c = Circuit().push(GateSDG(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── S† @ q[0]
<BLANKLINE>
>>> GateSDG().power(2), GateSDG().inverse()
(S†**2, S)
>>> GateSDG().decompose()
1-qubit circuit with 1 instructions:
└── U(0, 0, (-1/2)*pi, 0.0) @ q[0]
<BLANKLINE>
"""
def __init__(self):
super().__init__(GateS())
[docs]
def isopalias(self):
return True
[docs]
def inverse(self):
return GateS()
def _control(self, n):
return control_one_defined(n, self, mc.GateCSDG())
def _decompose(self, circ, qubits, bits):
q = qubits[0]
circ.push(GateU(0, 0, -pi / 2), q)
return circ