Source code for mimiqcircuits.operations.gates.standard.s
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from symengine import pi
import mimiqcircuits as mc
[docs]
def GateS():
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>
"""
return mc.Power(mc.GateZ(), 1 / 2)
mc.register_power_alias(mc.GateZ, 1 / 2, "S")
@mc.register_power_decomposition(mc.GateZ, 1 / 2)
def _decompose_gates(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateU(0, 0, pi / 2), q)
return circ
[docs]
def GateSDG():
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>
"""
return mc.Inverse(GateS())
@mc.register_inverse_decomposition((mc.Power, mc.GateZ, 1 / 2))
def _decompose_gatesdg(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateU(0, 0, -pi / 2), q)
return circ